Question 1

Consider the function   When   and   approximate to two decimal places the changed needed in n to compensate for

Accepted Answer

A)  -1.63 
B)  -0.62 
C)  -0.41 
D)  -0.15 
E)  -6.50 
A)  -1.63 
B)  -0.62 
C)  -0.41 
D)  -0.15 
E)  -6.50

Question 2

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.

Accepted Answer

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 
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

Question 3

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?

Accepted Answer

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. 
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 4

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

Accepted Answer

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. 
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 5

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?

Accepted Answer

A)    ; positive 
B)    ; positive 
C)    ; negative 
D)    ; negative 
E)    ; negative 
A)    ; positive 
B)    ; positive 
C)    ; negative 
D)    ; negative 
E)    ; negative

Question 6

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.

Accepted Answer

A)    
B)    
C)  144.52 
D)  23.69 
E)  -0.16 
A)    
B)    
C)  144.52 
D)  23.69 
E)  -0.16

Question 7

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?

Accepted Answer

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 8

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?

Accepted Answer

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 9

If   find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

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

Accepted Answer

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%. 
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 11

Consider the function   When   and   approximate to two decimal places the changed needed in n to compensate for

Accepted Answer

A)  -2.61 
B)  -0.38 
C)  -1.04 
D)  -0.15 
E)  -0.10 
A)  -2.61 
B)  -0.38 
C)  -1.04 
D)  -0.15 
E)  -0.10

Question 12

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.

Accepted Answer

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 13

If     .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

If   find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

If   find

Accepted Answer

A)    
B)    
C)    
D)    
E)  3 
A)    
B)    
C)    
D)    
E)  3

Question 17

If   find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

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

Accepted Answer

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. 
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 19

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.

Accepted Answer

A)  -4.25 
B)  0.24 
C)    
D)    
E)  7.66 
A)  -4.25 
B)  0.24 
C)    
D)    
E)  7.66

Question 20

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

Accepted Answer

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. 
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.

Consider the function When and approximate to two decimal places the changed needed in n to compensate for

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?

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.

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?

If find .

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

Consider the function When and approximate to two decimal places the changed needed in n to compensate for

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.

If .

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.

If find

If find

If find

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

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.

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

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Analyzing Multivariable Change: Optimization

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Exam 7: Ingredients of Multivariable Change: Models, Graphs, Rates

Consider the function When and approximate to two decimal places the changed needed in n to compensate for

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?

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.

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?

If find .

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

Consider the function When and approximate to two decimal places the changed needed in n to compensate for

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.

If .

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.

If find

If find

If find

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

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.

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

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Analyzing Multivariable Change: Optimization

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