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Deck 7: Ingredients of Multivariable Change: Models, Graphs, Rates
Full screen (f)
Question
Consider the graphs of 
below. At 
is 
decreasing when w decreases or when s decreases? Explain your answer. 
A)
decreases when w decreases because the lower valued contour curves are in that direction.
B)
decreases when w decreases because the contour curve slope is negative in that direction.
C)
decreases when w decreases because the rate of change is smaller in that direction.
D)
decreases when s decreases because the lower valued contour curves are in that direction.
E)
decreases when s decreases because the rate of change is smaller in that direction.
below. At is decreasing when w decreases or when s decreases? Explain your answer. A)
decreases when w decreases because the lower valued contour curves are in that direction.B)
decreases when w decreases because the contour curve slope is negative in that direction.C)
decreases when w decreases because the rate of change is smaller in that direction.D)
decreases when s decreases because the lower valued contour curves are in that direction.E)
decreases when s decreases because the rate of change is smaller in that direction.
Question
Consider any point 
on the contour graph of 
given below. Determine (if possible) what happens to the function output when x remains constant and y increases? 
A) The function decreases.
B) The function increases.
C) The function remains constant.
D) The function decreases and then increases.
E) Cannot be determined from the given information.
on the contour graph of given below. Determine (if possible) what happens to the function output when x remains constant and y increases? A) The function decreases.
B) The function increases.
C) The function remains constant.
D) The function decreases and then increases.
E) Cannot be determined from the given information.
Question
The table shows the number of hours of daylight for a given month at a given latitude (measured in degrees away from the equator) for the northern and southern hemispheres. How many hours of daylight will there be at a location at latitude 
north in March? 
A) 12.0
B) 12.6
C) 11.5
D) 12.1
E) 11.3
north in March? A) 12.0
B) 12.6
C) 11.5
D) 12.1
E) 11.3
Question
The function 
gives the capacity of a settled unopened silo in tons of silage when the silo has an inside diameter of d feet and the silage is h feet deep. Draw the 170-tons contour curve for d between 12 and 30 feet.
A)
B)
C)
D)
E)
gives the capacity of a settled unopened silo in tons of silage when the silo has an inside diameter of d feet and the silage is h feet deep. Draw the 170-tons contour curve for d between 12 and 30 feet.A)
B)
C)
D)
E)
Question
Consider the graphs of 
below. Determine, (if possible), if the change in 
will be greater when the position changed from 
to 
or when it changes from 
to 
A) The change is greater from
to 
B) The change is greater from
to 
C) The change is non-zero and approximately the same in both cases.
D) There is no change in either case.
E) Cannot be determined from the given information.
below. Determine, (if possible), if the change in will be greater when the position changed from to or when it changes from to A) The change is greater from
to B) The change is greater from
to C) The change is non-zero and approximately the same in both cases.
D) There is no change in either case.
E) Cannot be determined from the given information.
Question
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph and associated contour graph below show the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is 
Estimate the percentage of pigment removed from 20 grams of sunflower heads if the sunflower heads are washed for 5 minutes in 30 milliliters of water at 
A) 740%
B) 780%
C) 37%
D) 36%
E) 39%
Estimate the percentage of pigment removed from 20 grams of sunflower heads if the sunflower heads are washed for 5 minutes in 30 milliliters of water at A) 740%
B) 780%
C) 37%
D) 36%
E) 39%
Question
Draw the contour curves 
and 
for the multivariable function 
for 
A)
B)
C)
D)
E)
and for the multivariable function for A)
B)
C)
D)
E)
Question
Draw the contour curves 
, and 
for the multivariable function 
for 
A)
B)
C)
D)
E)
, and for the multivariable function for A)
B)
C)
D)
E)
Question
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph and associated contour graph below show the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is 
Estimate how much water would be necessary to remove 37% of pigment removed from 4 grams of sunflower heads if the sunflower heads are washed for 25 minutes at 
A) 30 milliliters
B) 30 milliliters or 120 milliliters
C) 30 milliliters or 39 milliliters
D) 120 milliliters or 156 milliliters
E) 156 milliliters
Estimate how much water would be necessary to remove 37% of pigment removed from 4 grams of sunflower heads if the sunflower heads are washed for 25 minutes at A) 30 milliliters
B) 30 milliliters or 120 milliliters
C) 30 milliliters or 39 milliliters
D) 120 milliliters or 156 milliliters
E) 156 milliliters
Question
The table shows the number of hours of daylight for a given month at a given latitude (measured in degrees away from the equator) for the northern and southern hemispheres. How many hours of daylight will there be in January in the region where you attend school? 
A) Answers will vary based on location of the school.
B) 6.8
C) 11.6
D) 12.1
E) 10.4
A) Answers will vary based on location of the school.
B) 6.8
C) 11.6
D) 12.1
E) 10.4
Question
Consider the point 
on the contour graph of 
given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve? 
A) decrease by 2
B) increase by 2
C) increase by 4
D) decrease by 4
E) no change is needed
on the contour graph of given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve? A) decrease by 2
B) increase by 2
C) increase by 4
D) decrease by 4
E) no change is needed
Question
Consider the point 
on the contour graph of 
given below. When y is decreased by 2, by what amount must x change in order to remain on the same contour curve? 
A) decrease by 1
B) increase by 1
C) increase by 3
D) decrease by 3
E) no change is needed
on the contour graph of given below. When y is decreased by 2, by what amount must x change in order to remain on the same contour curve? A) decrease by 1
B) increase by 1
C) increase by 3
D) decrease by 3
E) no change is needed
Question
The contour graph 
and its associated three-dimensional graph are given below. Determine (if possible) if the change in 
will be greater when 
shifts to 
or when 
shifts to 
A) Cannot be determined from the given information.
B) The change is approximately the same in both cases and is greater than zero.
C) There is no change in either case.
D) The shift from
to 
is greater.
E) The shift from
to 
is greater.
and its associated three-dimensional graph are given below. Determine (if possible) if the change in will be greater when shifts to or when shifts to A) Cannot be determined from the given information.
B) The change is approximately the same in both cases and is greater than zero.
C) There is no change in either case.
D) The shift from
to is greater.E) The shift from
to is greater. Question
The face value of a loan is 
dollars where the payment amount of 
dollars is paid 
times a year for 
years at 
interest. Rewrite 
as a model with two input variables.
A)
dollars is the face value of a loan for which the payment amount is 
dollars paid 12 times a year for 
years at 6% interest.
B)
dollars is the face value of a loan for which the payment amount is 
dollars paid 6 times a year for 
years at 12% interest.
C)
dollars is the face value of a loan for which the payment amount is 
dollars paid 12 times a year for 
years at 60% interest.
D)
dollars is the face value of a loan for which the payment amount is 
dollars paid 12 times a year for 
years at 0.6% interest.
E)
dollars is the face value of a loan for which the payment amount is 
dollars paid 6 times a year for 
years at 6% interest.
dollars where the payment amount of dollars is paid times a year for years at interest. Rewrite as a model with two input variables.A)
dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 6% interest.B)
dollars is the face value of a loan for which the payment amount is dollars paid 6 times a year for years at 12% interest.C)
dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 60% interest.D)
dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 0.6% interest.E)
dollars is the face value of a loan for which the payment amount is dollars paid 6 times a year for years at 6% interest. Question
The contour graph 
and its associated three-dimensional graph are given below. At 
will 
decrease more quickly as x decreases or as y decreases? Justify your answer. 
A)
decreases at the same rate in both directions because the contours are parabolic.
B)
will decrease more quickly when x decreases because the difference in contours is greater in that direction.
C)
will decrease more quickly when x decreases because the contours have negative slope in that direction.
D)
will decrease more quickly when y decreases because the difference in contours is greater in that direction.
E)
will decrease more quickly when y decreases because the contours have negative slope in that direction.
and its associated three-dimensional graph are given below. At will decrease more quickly as x decreases or as y decreases? Justify your answer. A)
decreases at the same rate in both directions because the contours are parabolic.B)
will decrease more quickly when x decreases because the difference in contours is greater in that direction.C)
will decrease more quickly when x decreases because the contours have negative slope in that direction.D)
will decrease more quickly when y decreases because the difference in contours is greater in that direction.E)
will decrease more quickly when y decreases because the contours have negative slope in that direction. Question
The contour graph 
and its associated three-dimensional graph are given below. At 
does 
increase when x increases or when x decreases? Justify your answer. 
A)
increases in both directions because the contours are parabolic.
B)
increase when x increases because the contours are nearly vertical.
C)
increase when x increases because the contours increase in that direction.
D)
increase when x decreases because the contours are nearly vertical.
E)
increase when x decreases because the contours increase in that direction.
and its associated three-dimensional graph are given below. At does increase when x increases or when x decreases? Justify your answer. A)
increases in both directions because the contours are parabolic.B)
increase when x increases because the contours are nearly vertical.C)
increase when x increases because the contours increase in that direction.D)
increase when x decreases because the contours are nearly vertical.E)
increase when x decreases because the contours increase in that direction. Question
Let 
be the profit in dollars from the sale of 1 meter of carpet when c dollars is the production cost per meter and s dollars is the selling price per meter. Write a sentence interpreting the mathematical notation 
A) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $4.50 per meter will result in $2.00 in profit.
B) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $2.00 per meter will result in $4.50 in profit.
C) Selling 1.3 meters of carpet at $4.50 per meter results in $2.00 profit.
D) Selling 4.5 meters of carpet at $1.30 per meter results in $2.00 profit.
E) When carpet costs $1.30 per meter to produce, 2 meters of carpet must be sold at $4.50 per meter in order to make a profit.
be the profit in dollars from the sale of 1 meter of carpet when c dollars is the production cost per meter and s dollars is the selling price per meter. Write a sentence interpreting the mathematical notation A) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $4.50 per meter will result in $2.00 in profit.
B) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $2.00 per meter will result in $4.50 in profit.
C) Selling 1.3 meters of carpet at $4.50 per meter results in $2.00 profit.
D) Selling 4.5 meters of carpet at $1.30 per meter results in $2.00 profit.
E) When carpet costs $1.30 per meter to produce, 2 meters of carpet must be sold at $4.50 per meter in order to make a profit.
Question
The figures show the profit (in hundred dollars) to craft fair organizers when 
hundred daily admission tickets and 
hundred weekend admission tickets to a large craft fair are purchased. Estimate the output value for point 
. 
A) 187
B) 154
C) 107
D) 60
E) 124
hundred daily admission tickets and hundred weekend admission tickets to a large craft fair are purchased. Estimate the output value for point . A) 187
B) 154
C) 107
D) 60
E) 124
Question
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph below shows the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is 
Find and interpret the input and output values for the point A. 
A) Input:
Output: 38
Interpretation: Washing the sunflower head for 12 minutes in 32 milliliters of water per gram of sunflower heads removes 38% of the pigment.
B) Input:
Output: 38
Interpretation: Washing the sunflower head for 32 minutes in 12 milliliters of water per gram of sunflower heads removes 38% of the pigment.
C) Input:
Output: 38
Interpretation: Washing the sunflower head for 35 minutes in 10 milliliters of water per gram of sunflower heads removes 38% of the pigment.
D) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 62% of the pigment.
E) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 38% of the pigment.
Find and interpret the input and output values for the point A. A) Input:
Output: 38
Interpretation: Washing the sunflower head for 12 minutes in 32 milliliters of water per gram of sunflower heads removes 38% of the pigment.
B) Input:
Output: 38
Interpretation: Washing the sunflower head for 32 minutes in 12 milliliters of water per gram of sunflower heads removes 38% of the pigment.
C) Input:
Output: 38
Interpretation: Washing the sunflower head for 35 minutes in 10 milliliters of water per gram of sunflower heads removes 38% of the pigment.
D) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 62% of the pigment.
E) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 38% of the pigment.
Question
Consider the table of apparent temperatures (given below), which shows the apparent temperature (how hot it feels) given air temperature and dew point. In order to model apparent temperature as a function of the dew point when the air temperature is 
which variable must be held constant? 
A) air temperature
B) dew point
C) apparent temperature
D)
E) no variables are held constant
which variable must be held constant? A) air temperature
B) dew point
C) apparent temperature
D)
E) no variables are held constant
Question
If 
find 
and 
.
A)
B)
C)
D)
E)
find and .A)
B)
C)
D)
E)
Question
The table shows per capita peach consumption. Find a cross-sectional model for a yearly income of $40,000. 
A)
pounds
B)
pounds
C)
pounds
D)
pounds
E)
pounds
A)
poundsB)
poundsC)
poundsD)
poundsE)
pounds Question
Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of Coke products, based on the prices of the products in the two machines are shown in the table below. Find an appropriate cross sectional model to estimate the sales of Coke products when the price of Coke is $1.50. 
A)
cans per day, where p is the cost of Pepsi
B)
cans per day, where p is the cost of Coke
C)
cans per day, where p is the cost of Pepsi
D)
cans per day, where p is the cost of Pepsi
E)
cans per day, where p is the cost of Coke
A)
cans per day, where p is the cost of PepsiB)
cans per day, where p is the cost of CokeC)
cans per day, where p is the cost of PepsiD)
cans per day, where p is the cost of PepsiE)
cans per day, where p is the cost of Coke Question
The table shows per capita peach consumption. Calculate per capita peach consumption for families with a yearly income of $40,000, when the price of peaches is $1.55 per pound. 
A) 7.7 pounds
B) 7.5 pounds
C) 7.6 pounds
D) 6.8 pounds
E) 6.4 pounds
A) 7.7 pounds
B) 7.5 pounds
C) 7.6 pounds
D) 6.8 pounds
E) 6.4 pounds
Question
If 
find 
.
A)
B)
C)
D)
E)
find .A)
B)
C)
D)
E)
Question
The table below gives the value 
of an investment of P dollars after 2 years in an account whose annual percentage yield is 100r%. The value of a $10,000 investment after 2 years can be modeled by 
Find and interpret 
when the annual interest rate is 4.3%. 
A) $8.30 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
B) $1,060.00 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
C) $1,060.00 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
D) $208.60 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
E) $104.30 per percentage point; it represents how much money in the investment is due to the interest rate.
of an investment of P dollars after 2 years in an account whose annual percentage yield is 100r%. The value of a $10,000 investment after 2 years can be modeled by Find and interpret when the annual interest rate is 4.3%. A) $8.30 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
B) $1,060.00 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
C) $1,060.00 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
D) $208.60 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
E) $104.30 per percentage point; it represents how much money in the investment is due to the interest rate.
Question
If 
find 
.
A)
B)
C)
D)
E)
find .A)
B)
C)
D)
E)
Question
Given the function 
consider the contour curve 
for 
What is the slope of the tangent line at 
Round your answer to two decimal places where appropriate.
A) -4.25
B) 0.24
C)
D)
E) 7.66
consider the contour curve for What is the slope of the tangent line at Round your answer to two decimal places where appropriate.A) -4.25
B) 0.24
C)
D)
E) 7.66
Question
If 
find 
A)
B)
C)
D)
E)
find A)
B)
C)
D)
E)
Question
The per capita consumption of peaches can be modeled as 
where the price of peaches 
is and the person lives in a family with annual income $10,000i. Use this model to calculate the rate of change of the per capita consumption of peaches with respect to yearly income when the yearly income is $30,000 and the price is $1.70 per pound.
A) 0.67 pound per ten thousand dollars
B) 0.47 pound per ten thousand dollars
C) 0.57 pound per ten thousand dollars
D) 0.51 pound per ten thousand dollars
E) 0.87 pound per ten thousand dollars
where the price of peaches is and the person lives in a family with annual income $10,000i. Use this model to calculate the rate of change of the per capita consumption of peaches with respect to yearly income when the yearly income is $30,000 and the price is $1.70 per pound.A) 0.67 pound per ten thousand dollars
B) 0.47 pound per ten thousand dollars
C) 0.57 pound per ten thousand dollars
D) 0.51 pound per ten thousand dollars
E) 0.87 pound per ten thousand dollars
Question
Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of coke products, based on the prices of the products in the two machines can be modeled by the equation 
cans per day, when Coke products cost $c and Pepsi products cost $p. Find and interpret 
A)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $1 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.
B)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $0.90 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.
C)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will decrease by about 81 cans.
D)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $0.80 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans.
E)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans.
cans per day, when Coke products cost $c and Pepsi products cost $p. Find and interpret A)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $1 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.B)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $0.90 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.C)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will decrease by about 81 cans.D)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $0.80 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans.E)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans. Question
Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of Coke products, based on the prices of the products in the two machines are shown in the table below. In order to estimate the sales of Coke products when the price of Coke is $0.75, which variable should be held constant? 
A) no variables need to be held constant
B) the daily sales of Coke products
C) the cost of Coke and Pepsi
D) the cost of Coke
E) the cost of Pepsi
A) no variables need to be held constant
B) the daily sales of Coke products
C) the cost of Coke and Pepsi
D) the cost of Coke
E) the cost of Pepsi
Question
If 
find 
A)
B)
C)
D)
E) 3
find A)
B)
C)
D)
E) 3
Question
The value 
of an investment of P dollars after 4 years in an account with annual percentage yield 100r% is given by the function 
dollars. Find and interpret 
A)
shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.
B)
is the cross-sectional model representing the value of $10,000 invested 4 years, as a function of the annual percentage yield, 100r%.
C)
represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%.
D)
shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.
E)
represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%.
of an investment of P dollars after 4 years in an account with annual percentage yield 100r% is given by the function dollars. Find and interpret A)
shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.B)
is the cross-sectional model representing the value of $10,000 invested 4 years, as a function of the annual percentage yield, 100r%.C)
represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%.D)
shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.E)
represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%. Question
If 
find 
A)
B)
C)
D)
E)
find A)
B)
C)
D)
E)
Question
If 
find 
.
A)
B)
C)
D)
E)
find .A)
B)
C)
D)
E)
Question
Find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The value 
of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function 
dollars. Write the partial derivative 
A)
B)
C)
D)
E)
of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function dollars. Write the partial derivative A)
B)
C)
D)
E)
Question
Consider the table of apparent temperatures (given below), which shows the apparent temperature (how hot it feels) given air temperature and dew point. Consider a model of the apparent temperature as a function of the dew point when the air temperature is 
How is this information represented in the table? 
A) as a column
B) as a row
C) as a cell
D) by the entire table
E) by a row and a column
How is this information represented in the table? A) as a column
B) as a row
C) as a cell
D) by the entire table
E) by a row and a column
Question
If 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Consider the function 
When 
and 
approximate to two decimal places the changed needed in n to compensate for 
A) -2.61
B) -0.38
C) -1.04
D) -0.15
E) -0.10
When and approximate to two decimal places the changed needed in n to compensate for A) -2.61
B) -0.38
C) -1.04
D) -0.15
E) -0.10
Question
Consider the function 
When 
and 
approximate to two decimal places the changed needed in n to compensate for 
A) -1.63
B) -0.62
C) -0.41
D) -0.15
E) -6.50
When and approximate to two decimal places the changed needed in n to compensate for A) -1.63
B) -0.62
C) -0.41
D) -0.15
E) -6.50
Question
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. Suppose that the percentage of the pigment that can be removed from a sunflower head by washing for 15 minutes can be modeled by 
percent where r milliliters of 
water is used for each gram of sunflower heads. Write a formula for the rate of change in the amount of water used with respect to a change in temperature when 47% of pigment is removed.
A)
B)
C)
D)
E)
percent where r milliliters of water is used for each gram of sunflower heads. Write a formula for the rate of change in the amount of water used with respect to a change in temperature when 47% of pigment is removed.A)
B)
C)
D)
E)
Question
The cost of having specialty T-shirts made depends on the number of colors used in the T-shirt design and the number of T-shirts being ordered. A function giving A, the average cost per T-shirt, when c colors are used and n T-shirts are ordered is 
dollars. Find a formula for 
If the average cost is to remain constant, would you expect 
to be positive or negative?
A)
; positive
B)
; positive
C)
; negative
D)
; negative
E)
; negative
dollars. Find a formula for If the average cost is to remain constant, would you expect to be positive or negative?A)
; positiveB)
; positiveC)
; negativeD)
; negativeE)
; negative Question
Given the function 
consider the contour curve 
for 
and 
What is the slope of the tangent line at 
Round your answer to two decimal places where appropriate.
A)
B)
C) 144.52
D) 23.69
E) -0.16
consider the contour curve for and What is the slope of the tangent line at Round your answer to two decimal places where appropriate.A)
B)
C) 144.52
D) 23.69
E) -0.16
Question
The cost of having specialty T-shirts made depends on the number of colors used in the T-shirt design and the number of T-shirts being ordered. A function giving A, the average cost per T-shirt, when c colors are used and n T-shirts are ordered is 
dollars. If 350 T-shirts are printed with six colors, determine (to the nearest hundredth of a cent) how quickly the average cost is changing when more T-shirts are printed.
A) 0.02 cents per T-shirt
B) -0.10 cents per T-shirt
C) 0.99 cents per T-shirt
D) -0.12 cents per T-shirt
E) -0.03 cents per T-shirt
dollars. If 350 T-shirts are printed with six colors, determine (to the nearest hundredth of a cent) how quickly the average cost is changing when more T-shirts are printed.A) 0.02 cents per T-shirt
B) -0.10 cents per T-shirt
C) 0.99 cents per T-shirt
D) -0.12 cents per T-shirt
E) -0.03 cents per T-shirt
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Deck 7: Ingredients of Multivariable Change: Models, Graphs, Rates
1
Consider the graphs of below. At is decreasing when w decreases or when s decreases? Explain your answer.
A) decreases when w decreases because the lower valued contour curves are in that direction.
B) decreases when w decreases because the contour curve slope is negative in that direction.
C) decreases when w decreases because the rate of change is smaller in that direction.
D) decreases when s decreases because the lower valued contour curves are in that direction.
E) decreases when s decreases because the rate of change is smaller in that direction.
below. At is decreasing when w decreases or when s decreases? Explain your answer. A)
decreases when w decreases because the lower valued contour curves are in that direction.B)
decreases when w decreases because the contour curve slope is negative in that direction.C)
decreases when w decreases because the rate of change is smaller in that direction.D)
decreases when s decreases because the lower valued contour curves are in that direction.E)
decreases when s decreases because the rate of change is smaller in that direction. decreases when s decreases because the lower valued contour curves are in that direction. 2
Consider any point on the contour graph of given below. Determine (if possible) what happens to the function output when x remains constant and y increases?
A) The function decreases.
B) The function increases.
C) The function remains constant.
D) The function decreases and then increases.
E) Cannot be determined from the given information.
on the contour graph of given below. Determine (if possible) what happens to the function output when x remains constant and y increases? A) The function decreases.
B) The function increases.
C) The function remains constant.
D) The function decreases and then increases.
E) Cannot be determined from the given information.
The function decreases.
3
The table shows the number of hours of daylight for a given month at a given latitude (measured in degrees away from the equator) for the northern and southern hemispheres. How many hours of daylight will there be at a location at latitude north in March?
A) 12.0
B) 12.6
C) 11.5
D) 12.1
E) 11.3
north in March? A) 12.0
B) 12.6
C) 11.5
D) 12.1
E) 11.3
12.0
4
The function gives the capacity of a settled unopened silo in tons of silage when the silo has an inside diameter of d feet and the silage is h feet deep. Draw the 170-tons contour curve for d between 12 and 30 feet.
A)
B)
C)
D)
E)
gives the capacity of a settled unopened silo in tons of silage when the silo has an inside diameter of d feet and the silage is h feet deep. Draw the 170-tons contour curve for d between 12 and 30 feet.A)
B)
C)
D)
E)
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5
Consider the graphs of below. Determine, (if possible), if the change in will be greater when the position changed from to or when it changes from to
A) The change is greater from to
B) The change is greater from to
C) The change is non-zero and approximately the same in both cases.
D) There is no change in either case.
E) Cannot be determined from the given information.
below. Determine, (if possible), if the change in will be greater when the position changed from to or when it changes from to A) The change is greater from
to B) The change is greater from
to C) The change is non-zero and approximately the same in both cases.
D) There is no change in either case.
E) Cannot be determined from the given information.
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6
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph and associated contour graph below show the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is Estimate the percentage of pigment removed from 20 grams of sunflower heads if the sunflower heads are washed for 5 minutes in 30 milliliters of water at
A) 740%
B) 780%
C) 37%
D) 36%
E) 39%
Estimate the percentage of pigment removed from 20 grams of sunflower heads if the sunflower heads are washed for 5 minutes in 30 milliliters of water at A) 740%
B) 780%
C) 37%
D) 36%
E) 39%
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7
Draw the contour curves and for the multivariable function for
A)
B)
C)
D)
E)
and for the multivariable function for A)
B)
C)
D)
E)
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8
Draw the contour curves , and for the multivariable function for
A)
B)
C)
D)
E)
, and for the multivariable function for A)
B)
C)
D)
E)
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9
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph and associated contour graph below show the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is Estimate how much water would be necessary to remove 37% of pigment removed from 4 grams of sunflower heads if the sunflower heads are washed for 25 minutes at
A) 30 milliliters
B) 30 milliliters or 120 milliliters
C) 30 milliliters or 39 milliliters
D) 120 milliliters or 156 milliliters
E) 156 milliliters
Estimate how much water would be necessary to remove 37% of pigment removed from 4 grams of sunflower heads if the sunflower heads are washed for 25 minutes at A) 30 milliliters
B) 30 milliliters or 120 milliliters
C) 30 milliliters or 39 milliliters
D) 120 milliliters or 156 milliliters
E) 156 milliliters
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10
The table shows the number of hours of daylight for a given month at a given latitude (measured in degrees away from the equator) for the northern and southern hemispheres. How many hours of daylight will there be in January in the region where you attend school?
A) Answers will vary based on location of the school.
B) 6.8
C) 11.6
D) 12.1
E) 10.4
A) Answers will vary based on location of the school.
B) 6.8
C) 11.6
D) 12.1
E) 10.4
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11
Consider the point on the contour graph of given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve?
A) decrease by 2
B) increase by 2
C) increase by 4
D) decrease by 4
E) no change is needed
on the contour graph of given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve? A) decrease by 2
B) increase by 2
C) increase by 4
D) decrease by 4
E) no change is needed
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12
Consider the point on the contour graph of given below. When y is decreased by 2, by what amount must x change in order to remain on the same contour curve?
A) decrease by 1
B) increase by 1
C) increase by 3
D) decrease by 3
E) no change is needed
on the contour graph of given below. When y is decreased by 2, by what amount must x change in order to remain on the same contour curve? A) decrease by 1
B) increase by 1
C) increase by 3
D) decrease by 3
E) no change is needed
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13
The contour graph and its associated three-dimensional graph are given below. Determine (if possible) if the change in will be greater when shifts to or when shifts to
A) Cannot be determined from the given information.
B) The change is approximately the same in both cases and is greater than zero.
C) There is no change in either case.
D) The shift from to is greater.
E) The shift from to is greater.
and its associated three-dimensional graph are given below. Determine (if possible) if the change in will be greater when shifts to or when shifts to A) Cannot be determined from the given information.
B) The change is approximately the same in both cases and is greater than zero.
C) There is no change in either case.
D) The shift from
to is greater.E) The shift from
to is greater. Unlock Deck
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14
The face value of a loan is dollars where the payment amount of dollars is paid times a year for years at interest. Rewrite as a model with two input variables.
A) dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 6% interest.
B) dollars is the face value of a loan for which the payment amount is dollars paid 6 times a year for years at 12% interest.
C) dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 60% interest.
D) dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 0.6% interest.
E) dollars is the face value of a loan for which the payment amount is dollars paid 6 times a year for years at 6% interest.
dollars where the payment amount of dollars is paid times a year for years at interest. Rewrite as a model with two input variables.A)
dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 6% interest.B)
dollars is the face value of a loan for which the payment amount is dollars paid 6 times a year for years at 12% interest.C)
dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 60% interest.D)
dollars is the face value of a loan for which the payment amount is dollars paid 12 times a year for years at 0.6% interest.E)
dollars is the face value of a loan for which the payment amount is dollars paid 6 times a year for years at 6% interest. Unlock Deck
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15
The contour graph and its associated three-dimensional graph are given below. At will decrease more quickly as x decreases or as y decreases? Justify your answer.
A) decreases at the same rate in both directions because the contours are parabolic.
B) will decrease more quickly when x decreases because the difference in contours is greater in that direction.
C) will decrease more quickly when x decreases because the contours have negative slope in that direction.
D) will decrease more quickly when y decreases because the difference in contours is greater in that direction.
E) will decrease more quickly when y decreases because the contours have negative slope in that direction.
and its associated three-dimensional graph are given below. At will decrease more quickly as x decreases or as y decreases? Justify your answer. A)
decreases at the same rate in both directions because the contours are parabolic.B)
will decrease more quickly when x decreases because the difference in contours is greater in that direction.C)
will decrease more quickly when x decreases because the contours have negative slope in that direction.D)
will decrease more quickly when y decreases because the difference in contours is greater in that direction.E)
will decrease more quickly when y decreases because the contours have negative slope in that direction. Unlock Deck
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16
The contour graph and its associated three-dimensional graph are given below. At does increase when x increases or when x decreases? Justify your answer.
A) increases in both directions because the contours are parabolic.
B) increase when x increases because the contours are nearly vertical.
C) increase when x increases because the contours increase in that direction.
D) increase when x decreases because the contours are nearly vertical.
E) increase when x decreases because the contours increase in that direction.
and its associated three-dimensional graph are given below. At does increase when x increases or when x decreases? Justify your answer. A)
increases in both directions because the contours are parabolic.B)
increase when x increases because the contours are nearly vertical.C)
increase when x increases because the contours increase in that direction.D)
increase when x decreases because the contours are nearly vertical.E)
increase when x decreases because the contours increase in that direction. Unlock Deck
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17
Let be the profit in dollars from the sale of 1 meter of carpet when c dollars is the production cost per meter and s dollars is the selling price per meter. Write a sentence interpreting the mathematical notation
A) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $4.50 per meter will result in $2.00 in profit.
B) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $2.00 per meter will result in $4.50 in profit.
C) Selling 1.3 meters of carpet at $4.50 per meter results in $2.00 profit.
D) Selling 4.5 meters of carpet at $1.30 per meter results in $2.00 profit.
E) When carpet costs $1.30 per meter to produce, 2 meters of carpet must be sold at $4.50 per meter in order to make a profit.
be the profit in dollars from the sale of 1 meter of carpet when c dollars is the production cost per meter and s dollars is the selling price per meter. Write a sentence interpreting the mathematical notation A) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $4.50 per meter will result in $2.00 in profit.
B) When carpet costs $1.30 per meter to produce, the sale of 1 meter at $2.00 per meter will result in $4.50 in profit.
C) Selling 1.3 meters of carpet at $4.50 per meter results in $2.00 profit.
D) Selling 4.5 meters of carpet at $1.30 per meter results in $2.00 profit.
E) When carpet costs $1.30 per meter to produce, 2 meters of carpet must be sold at $4.50 per meter in order to make a profit.
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18
The figures show the profit (in hundred dollars) to craft fair organizers when hundred daily admission tickets and hundred weekend admission tickets to a large craft fair are purchased. Estimate the output value for point .
A) 187
B) 154
C) 107
D) 60
E) 124
hundred daily admission tickets and hundred weekend admission tickets to a large craft fair are purchased. Estimate the output value for point . A) 187
B) 154
C) 107
D) 60
E) 124
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19
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. The three dimensional graph below shows the percentage of pigment that can be removed from the sunflower head by washing it for t minutes in r milliliters of water per gram of sunflower heads when the water temperature is Find and interpret the input and output values for the point A.
A) Input:
Output: 38
Interpretation: Washing the sunflower head for 12 minutes in 32 milliliters of water per gram of sunflower heads removes 38% of the pigment.
B) Input:
Output: 38
Interpretation: Washing the sunflower head for 32 minutes in 12 milliliters of water per gram of sunflower heads removes 38% of the pigment.
C) Input:
Output: 38
Interpretation: Washing the sunflower head for 35 minutes in 10 milliliters of water per gram of sunflower heads removes 38% of the pigment.
D) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 62% of the pigment.
E) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 38% of the pigment.
Find and interpret the input and output values for the point A. A) Input:
Output: 38
Interpretation: Washing the sunflower head for 12 minutes in 32 milliliters of water per gram of sunflower heads removes 38% of the pigment.
B) Input:
Output: 38
Interpretation: Washing the sunflower head for 32 minutes in 12 milliliters of water per gram of sunflower heads removes 38% of the pigment.
C) Input:
Output: 38
Interpretation: Washing the sunflower head for 35 minutes in 10 milliliters of water per gram of sunflower heads removes 38% of the pigment.
D) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 62% of the pigment.
E) Input:
Output: 38
Interpretation: Washing the sunflower head for 10 minutes in 35 milliliters of water per gram of sunflower heads removes 38% of the pigment.
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20
Consider the table of apparent temperatures (given below), which shows the apparent temperature (how hot it feels) given air temperature and dew point. In order to model apparent temperature as a function of the dew point when the air temperature is which variable must be held constant?
A) air temperature
B) dew point
C) apparent temperature
D)
E) no variables are held constant
which variable must be held constant? A) air temperature
B) dew point
C) apparent temperature
D)
E) no variables are held constant
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21
If find and .
A)
B)
C)
D)
E)
find and .A)
B)
C)
D)
E)
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22
The table shows per capita peach consumption. Find a cross-sectional model for a yearly income of $40,000.
A) pounds
B) pounds
C) pounds
D) pounds
E) pounds
A)
poundsB)
poundsC)
poundsD)
poundsE)
pounds Unlock Deck
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23
Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of Coke products, based on the prices of the products in the two machines are shown in the table below. Find an appropriate cross sectional model to estimate the sales of Coke products when the price of Coke is $1.50.
A) cans per day, where p is the cost of Pepsi
B) cans per day, where p is the cost of Coke
C) cans per day, where p is the cost of Pepsi
D) cans per day, where p is the cost of Pepsi
E) cans per day, where p is the cost of Coke
A)
cans per day, where p is the cost of PepsiB)
cans per day, where p is the cost of CokeC)
cans per day, where p is the cost of PepsiD)
cans per day, where p is the cost of PepsiE)
cans per day, where p is the cost of Coke Unlock Deck
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24
The table shows per capita peach consumption. Calculate per capita peach consumption for families with a yearly income of $40,000, when the price of peaches is $1.55 per pound.
A) 7.7 pounds
B) 7.5 pounds
C) 7.6 pounds
D) 6.8 pounds
E) 6.4 pounds
A) 7.7 pounds
B) 7.5 pounds
C) 7.6 pounds
D) 6.8 pounds
E) 6.4 pounds
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25
If find .
A)
B)
C)
D)
E)
find .A)
B)
C)
D)
E)
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26
The table below gives the value of an investment of P dollars after 2 years in an account whose annual percentage yield is 100r%. The value of a $10,000 investment after 2 years can be modeled by Find and interpret when the annual interest rate is 4.3%.
A) $8.30 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
B) $1,060.00 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
C) $1,060.00 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
D) $208.60 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
E) $104.30 per percentage point; it represents how much money in the investment is due to the interest rate.
of an investment of P dollars after 2 years in an account whose annual percentage yield is 100r%. The value of a $10,000 investment after 2 years can be modeled by Find and interpret when the annual interest rate is 4.3%. A) $8.30 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
B) $1,060.00 per percentage point; it represents how much money a $10,000 investment would earn if the interest rate increased by one percent.
C) $1,060.00 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
D) $208.60 per percentage point; it represents the rate of increase in value of $10,000 investment as the interest rate increases by one percent.
E) $104.30 per percentage point; it represents how much money in the investment is due to the interest rate.
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27
If find .
A)
B)
C)
D)
E)
find .A)
B)
C)
D)
E)
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28
Given the function consider the contour curve for What is the slope of the tangent line at Round your answer to two decimal places where appropriate.
A) -4.25
B) 0.24
C)
D)
E) 7.66
consider the contour curve for What is the slope of the tangent line at Round your answer to two decimal places where appropriate.A) -4.25
B) 0.24
C)
D)
E) 7.66
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29
If find
A)
B)
C)
D)
E)
find A)
B)
C)
D)
E)
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30
The per capita consumption of peaches can be modeled as where the price of peaches is and the person lives in a family with annual income $10,000i. Use this model to calculate the rate of change of the per capita consumption of peaches with respect to yearly income when the yearly income is $30,000 and the price is $1.70 per pound.
A) 0.67 pound per ten thousand dollars
B) 0.47 pound per ten thousand dollars
C) 0.57 pound per ten thousand dollars
D) 0.51 pound per ten thousand dollars
E) 0.87 pound per ten thousand dollars
where the price of peaches is and the person lives in a family with annual income $10,000i. Use this model to calculate the rate of change of the per capita consumption of peaches with respect to yearly income when the yearly income is $30,000 and the price is $1.70 per pound.A) 0.67 pound per ten thousand dollars
B) 0.47 pound per ten thousand dollars
C) 0.57 pound per ten thousand dollars
D) 0.51 pound per ten thousand dollars
E) 0.87 pound per ten thousand dollars
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31
Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of coke products, based on the prices of the products in the two machines can be modeled by the equation cans per day, when Coke products cost $c and Pepsi products cost $p. Find and interpret
A) means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $1 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.
B) means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $0.90 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.
C) means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will decrease by about 81 cans.
D) means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $0.80 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans.
E) means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans.
cans per day, when Coke products cost $c and Pepsi products cost $p. Find and interpret A)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $1 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.B)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Coke products increases by $0.90 while the price of Pepsi products remains constant, then the daily sale of Coke products will decrease by about 81 cans.C)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will decrease by about 81 cans.D)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $0.80 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans.E)
means that when the price of Pepsi products is $0.80 and the price of Coke products is $0.90, if the price of Pepsi products increases by $1 while the price of Coke products remains constant, then the daily sale of Coke products will increase by about 194 cans. Unlock Deck
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32
Two vending machines sit side by side in a a college dorm. One machine sells Coke products and the other sells Pepsi products. Daily sales of Coke products, based on the prices of the products in the two machines are shown in the table below. In order to estimate the sales of Coke products when the price of Coke is $0.75, which variable should be held constant?
A) no variables need to be held constant
B) the daily sales of Coke products
C) the cost of Coke and Pepsi
D) the cost of Coke
E) the cost of Pepsi
A) no variables need to be held constant
B) the daily sales of Coke products
C) the cost of Coke and Pepsi
D) the cost of Coke
E) the cost of Pepsi
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33
If find
A)
B)
C)
D)
E) 3
find A)
B)
C)
D)
E) 3
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34
The value of an investment of P dollars after 4 years in an account with annual percentage yield 100r% is given by the function dollars. Find and interpret
A) shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.
B) is the cross-sectional model representing the value of $10,000 invested 4 years, as a function of the annual percentage yield, 100r%.
C) represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%.
D) shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.
E) represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%.
of an investment of P dollars after 4 years in an account with annual percentage yield 100r% is given by the function dollars. Find and interpret A)
shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.B)
is the cross-sectional model representing the value of $10,000 invested 4 years, as a function of the annual percentage yield, 100r%.C)
represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%.D)
shows how the value of a $10,000 investment changes as the yield rate, 100r%, changes.E)
represents how much money a $10,000 investment earned after 4 years at an annual percentage yield rate of 100r%. Unlock Deck
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35
If find
A)
B)
C)
D)
E)
find A)
B)
C)
D)
E)
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36
If find .
A)
B)
C)
D)
E)
find .A)
B)
C)
D)
E)
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37
Find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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38
The value of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function dollars. Write the partial derivative
A)
B)
C)
D)
E)
of an investment of $4,000 after t years in an account for which the interest rate 100r% is compounded continuously is given by the function dollars. Write the partial derivative A)
B)
C)
D)
E)
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39
Consider the table of apparent temperatures (given below), which shows the apparent temperature (how hot it feels) given air temperature and dew point. Consider a model of the apparent temperature as a function of the dew point when the air temperature is How is this information represented in the table?
A) as a column
B) as a row
C) as a cell
D) by the entire table
E) by a row and a column
How is this information represented in the table? A) as a column
B) as a row
C) as a cell
D) by the entire table
E) by a row and a column
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40
If .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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41
Consider the function When and approximate to two decimal places the changed needed in n to compensate for
A) -2.61
B) -0.38
C) -1.04
D) -0.15
E) -0.10
When and approximate to two decimal places the changed needed in n to compensate for A) -2.61
B) -0.38
C) -1.04
D) -0.15
E) -0.10
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42
Consider the function When and approximate to two decimal places the changed needed in n to compensate for
A) -1.63
B) -0.62
C) -0.41
D) -0.15
E) -6.50
When and approximate to two decimal places the changed needed in n to compensate for A) -1.63
B) -0.62
C) -0.41
D) -0.15
E) -6.50
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43
A process to extract pectin and pigment from sunflower heads involves washing the sunflower heads in heated water. Suppose that the percentage of the pigment that can be removed from a sunflower head by washing for 15 minutes can be modeled by percent where r milliliters of water is used for each gram of sunflower heads. Write a formula for the rate of change in the amount of water used with respect to a change in temperature when 47% of pigment is removed.
A)
B)
C)
D)
E)
percent where r milliliters of water is used for each gram of sunflower heads. Write a formula for the rate of change in the amount of water used with respect to a change in temperature when 47% of pigment is removed.A)
B)
C)
D)
E)
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44
The cost of having specialty T-shirts made depends on the number of colors used in the T-shirt design and the number of T-shirts being ordered. A function giving A, the average cost per T-shirt, when c colors are used and n T-shirts are ordered is dollars. Find a formula for If the average cost is to remain constant, would you expect to be positive or negative?
A) ; positive
B) ; positive
C) ; negative
D) ; negative
E) ; negative
dollars. Find a formula for If the average cost is to remain constant, would you expect to be positive or negative?A)
; positiveB)
; positiveC)
; negativeD)
; negativeE)
; negative Unlock Deck
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45
Given the function consider the contour curve for and What is the slope of the tangent line at Round your answer to two decimal places where appropriate.
A)
B)
C) 144.52
D) 23.69
E) -0.16
consider the contour curve for and What is the slope of the tangent line at Round your answer to two decimal places where appropriate.A)
B)
C) 144.52
D) 23.69
E) -0.16
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46
The cost of having specialty T-shirts made depends on the number of colors used in the T-shirt design and the number of T-shirts being ordered. A function giving A, the average cost per T-shirt, when c colors are used and n T-shirts are ordered is dollars. If 350 T-shirts are printed with six colors, determine (to the nearest hundredth of a cent) how quickly the average cost is changing when more T-shirts are printed.
A) 0.02 cents per T-shirt
B) -0.10 cents per T-shirt
C) 0.99 cents per T-shirt
D) -0.12 cents per T-shirt
E) -0.03 cents per T-shirt
dollars. If 350 T-shirts are printed with six colors, determine (to the nearest hundredth of a cent) how quickly the average cost is changing when more T-shirts are printed.A) 0.02 cents per T-shirt
B) -0.10 cents per T-shirt
C) 0.99 cents per T-shirt
D) -0.12 cents per T-shirt
E) -0.03 cents per T-shirt
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Unlock Deck
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