Question 1

Determine whether the function is continuous or differentiable for given input values.

Accepted Answer

A)  The function is continuous on the input interval shown, but it is not differentiable at x = 4. 
B)  The function is continuous on the input interval shown, but it is not differentiable at x = 6. 
C)  The function is not continuous on the input interval shown, but it is not differentiable at x = 6. 
D)  The function is not continuous on the input interval shown, but it is not differentiable at x = 4. 
E)  The function is both continuous and differentiable at x = 4. 
A)  The function is continuous on the input interval shown, but it is not differentiable at x = 4. 
B)  The function is continuous on the input interval shown, but it is not differentiable at x = 6. 
C)  The function is not continuous on the input interval shown, but it is not differentiable at x = 6. 
D)  The function is not continuous on the input interval shown, but it is not differentiable at x = 4. 
E)  The function is both continuous and differentiable at x = 4.

Question 2

The function D gives the time, in years, that it takes for an investment to double if interest is continuously compounded at r%. Write a sentence of interpretation for

Accepted Answer

A)  At 8% interest compounded continuously, an investment will double its value in 7.2 years. 
B)  At 8% interest compounded continuously, an investment will triple its value in 7.2 years. 
C)  At 8% interest the investment will be same after 7.2 years. 
D)  At 7.2% interest compounded continuously, an investment will double its value in 8 years. 
E)  At 7.2% interest compounded continuously, an investment will triple its value in 8 years. 
A)  At 8% interest compounded continuously, an investment will double its value in 7.2 years. 
B)  At 8% interest compounded continuously, an investment will triple its value in 7.2 years. 
C)  At 8% interest the investment will be same after 7.2 years. 
D)  At 7.2% interest compounded continuously, an investment will double its value in 8 years. 
E)  At 7.2% interest compounded continuously, an investment will triple its value in 8 years.

Question 3

For a certain brand of bicycle,   Canadian dollars gives the profit from the sale of x mountain bikes. On June 27, 2009, P Canadian dollars were worth   American dollars. Assume that this conversion applies today. Calculate the profit in Canadian and in American dollars from the sale of 600 mountain bikes. Round your answer to two decimal places.

Accepted Answer

A)  $ 256.27 Canadian
$ 256.27 U. S. 
B)  $ 391.58 Canadian
$ 391.58 U. S. 
C)  $ 391.58 Canadian
$ 256.27 U. S. 
D)  $ 256.27 Canadian
$ 391.58 U. S. 
E)  $ 1.01 Canadian
$ 0)00 U. S. 
A)  $ 256.27 Canadian
$ 256.27 U. S. 
B)  $ 391.58 Canadian
$ 391.58 U. S. 
C)  $ 391.58 Canadian
$ 256.27 U. S. 
D)  $ 256.27 Canadian
$ 391.58 U. S. 
E)  $ 1.01 Canadian
$ 0)00 U. S.

Question 4

An Airline industry posted a profit of $17.8 million at the end of 2009 compared with a loss of $121.7 million in 2008. Calculate change.

Accepted Answer

A)  $139.5 million 
B)  $121.7 million 
C)  $103.9 million 
D)  $69.8 million 
A)  $139.5 million 
B)  $121.7 million 
C)  $103.9 million 
D)  $69.8 million

Question 5

At the indicated x-value, find the slope of the tangent line.

Accepted Answer

A)  75 
B)  245 
C)  26 
D)  33 
E)  47 
A)  75 
B)  245 
C)  26 
D)  33 
E)  47

Question 6

Calculate the average rate of change in disposable personal income between 1995 and 2000. Round your answer to the nearest dollar.

Accepted Answer

A)  2390 dollars per person per year 
B)  1195 dollars per person per year 
C)  3348 dollars per person per year 
D)  5150 dollars per person per year 
E)  1030 dollars per person per year 
A)  2390 dollars per person per year 
B)  1195 dollars per person per year 
C)  3348 dollars per person per year 
D)  5150 dollars per person per year 
E)  1030 dollars per person per year

Question 7

Use the figure to answer the questions.   Is the graph steeper at point C or at point E?

Accepted Answer

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

Question 8

Find the slope of the tangent to the graph of f (x) at any point.   estimate to the nearest tenth

Accepted Answer

A)  12.6 
B)  22.2 
C)  12.1 
D)  10.1 
E)  11.1 
A)  12.6 
B)  22.2 
C)  12.1 
D)  10.1 
E)  11.1

Question 9

Given the statement: The company lost $15,000 during the past 5 months.
Choose the sentence that best expresses how rapidly, on average, the quantity has changed over the given interval.

Accepted Answer

A)  The company lost on average $15,000 per month. 
B)  The company lost on average $75,000 per month. 
C)  The company lost on average $7,500 per month. 
D)  The company lost on average $8,000 per month. 
E)  The company lost on average $3,000 per month. 
A)  The company lost on average $15,000 per month. 
B)  The company lost on average $75,000 per month. 
C)  The company lost on average $7,500 per month. 
D)  The company lost on average $8,000 per month. 
E)  The company lost on average $3,000 per month.

Question 10

A graph of a model for the sales of services between 2004 and 2008 by Kelly Services, Inc., a leading global provider of staffing services, is shown below.   Use the graph to calculate the average rate of change in Kelly's sales of services between 2005 and 2007.

Accepted Answer

A)  241 million dollars per year 
B)  274 million dollars per year 
C)  5500 million dollars per year 
D)  550 million dollars per year 
E)  5 million dollars per year 
A)  241 million dollars per year 
B)  274 million dollars per year 
C)  5500 million dollars per year 
D)  550 million dollars per year 
E)  5 million dollars per year

Question 11

Find the derivative of the given function using the algebraic method.

Accepted Answer

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

Question 12

If   find   .

Accepted Answer

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

Question 13

Suppose the function G(t) represents a test grade (out of 100 points) as a function of hours studied. If   points, approximate, to one decimal place, the slope of the tangent line when   .

Accepted Answer

A)  87.2 points per hour 
B)  3.8 points per hour 
C)  21.9 points per hour 
D)  -0.5 points per hour 
E)  -7.1 points per hour 
A)  87.2 points per hour 
B)  3.8 points per hour 
C)  21.9 points per hour 
D)  -0.5 points per hour 
E)  -7.1 points per hour

Question 14

A chemical reaction begins when a certain mixture of chemicals reaches 95°C. The reaction activity is measured in units (U) per 100 microliters (100µL) of the mixture. Measurements during the first 18 minutes after the mixture reaches 95°C are listed in Table below. Chemical Reaction   The Logistic model for the above data is approximately given as     .
Estimate the average rate of change of the reaction activity between 5 minutes and 15 minutes. Round your answer to three decimal places.

Accepted Answer

A)  0.141   
B)  0.071   
C)  0.227   
D)  0.113   
E)  7.074   
A)  0.141   
B)  0.071   
C)  0.227   
D)  0.113   
E)  7.074

Question 15

The function P gives the profit in dollars that a fraternity makes selling x T-shirts. Is it possible for   to be negative? Explain.

Accepted Answer

A)    can be negative if the cost of the 80 shirts is greater than the revenue from the sales of 80 shirts. 
B)    can be negative if the cost of the 80 shirts is less than the revenue from the sales of 80 shirts. 
C)    can be negative if the cost of the 80 shirts is greater than or equal to the revenue from the sales of 80 shirts. 
D)    cannot be negative as the cost of the 80 shirts is less than the revenue from the sales of 80 shirts. 
E)    cannot be negative as the cost of the 80 shirts is greater than the revenue from the sales of 80 shirts. 
A)    can be negative if the cost of the 80 shirts is greater than the revenue from the sales of 80 shirts. 
B)    can be negative if the cost of the 80 shirts is less than the revenue from the sales of 80 shirts. 
C)    can be negative if the cost of the 80 shirts is greater than or equal to the revenue from the sales of 80 shirts. 
D)    cannot be negative as the cost of the 80 shirts is less than the revenue from the sales of 80 shirts. 
E)    cannot be negative as the cost of the 80 shirts is greater than the revenue from the sales of 80 shirts.

Question 16

The percentage of students meeting national mathematics benchmarks on the ACT increased from 39% in 2001 to 42% in 2010. Calculate the average rate of change. Round your answer to two decimal places.

Accepted Answer

A)  0.23 percentage points per year 
B)  0.33 percentage points per year 
C)  0.99 percentage points per year 
D)  0.08 percentage points per year 
E)  3.20 percentage points per year 
A)  0.23 percentage points per year 
B)  0.33 percentage points per year 
C)  0.99 percentage points per year 
D)  0.08 percentage points per year 
E)  3.20 percentage points per year

Question 17

An object is dropped off a building. Ignoring air resistance we know from physics that its height above ground t seconds after being dropped is given by Height   feet. Determine the object's velocity after 2.5 seconds.

Accepted Answer

A)  -80 feet per second 
B)  -50 feet per second 
C)  -20 feet per second 
D)  -16 feet per second 
E)  -32 feet per second 
A)  -80 feet per second 
B)  -50 feet per second 
C)  -20 feet per second 
D)  -16 feet per second 
E)  -32 feet per second

Question 18

The function g gives the fuel efficiency, in miles per gallon, of a car traveling v miles per hour. Write a sentence of interpretation for the following statement.   .

Accepted Answer

A)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is neither increasing nor decreasing for a car traveling 52 mph. 
B)  The fuel efficiency of a car traveling 52 is increasing by 0.25 mpg per mph.
The fuel efficiency is neither increasing nor decreasing for a car traveling 35 mph. 
C)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is increasing for a car traveling 52 mph. 
D)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is decreasing for a car traveling 52 mph. 
E)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is increasing or decreasing for a car traveling 35 mph. 
A)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is neither increasing nor decreasing for a car traveling 52 mph. 
B)  The fuel efficiency of a car traveling 52 is increasing by 0.25 mpg per mph.
The fuel efficiency is neither increasing nor decreasing for a car traveling 35 mph. 
C)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is increasing for a car traveling 52 mph. 
D)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is decreasing for a car traveling 52 mph. 
E)  The fuel efficiency of a car traveling 35 is increasing by 0.25 mpg per mph.
The fuel efficiency is increasing or decreasing for a car traveling 35 mph.

Question 19

The function D gives the time, in years, that it takes for an investment to double if interest is continuously compounded at r%. Write a sentence of interpretation for

Accepted Answer

A)  If the interest rate for an investment at 4% compounded continuously is changed to 5% compounded continuously, the doubling time will decrease by approximately 2.74 years. 
B)  If the interest rate for an investment at 4% compounded continuously the doubling time will decrease by approximately 2.74 years. 
C)  If the interest rate for an investment at 2.74% compounded continuously the doubling time will decrease by approximately 4 years. 
D)  If the interest rate for an investment at 4% compounded continuously is changed to 5% compounded continuously, the doubling time will increase by approximately 2.74 years. 
E)  If the interest rate for an investment at 2.74% compounded continuously is changed to 3.74% compounded continuously, the doubling time will increase by approximately 4 years. 
A)  If the interest rate for an investment at 4% compounded continuously is changed to 5% compounded continuously, the doubling time will decrease by approximately 2.74 years. 
B)  If the interest rate for an investment at 4% compounded continuously the doubling time will decrease by approximately 2.74 years. 
C)  If the interest rate for an investment at 2.74% compounded continuously the doubling time will decrease by approximately 4 years. 
D)  If the interest rate for an investment at 4% compounded continuously is changed to 5% compounded continuously, the doubling time will increase by approximately 2.74 years. 
E)  If the interest rate for an investment at 2.74% compounded continuously is changed to 3.74% compounded continuously, the doubling time will increase by approximately 4 years.

Question 20

If   find   .

Accepted Answer

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

Determine whether the function is continuous or differentiable for given input values.

The function D gives the time, in years, that it takes for an investment to double if interest is continuously compounded at r%. Write a sentence of interpretation for

An Airline industry posted a profit of $17.8 million at the end of 2009 compared with a loss of $121.7 million in 2008. Calculate change.

At the indicated x-value, find the slope of the tangent line.

Calculate the average rate of change in disposable personal income between 1995 and 2000. Round your answer to the nearest dollar.

Use the figure to answer the questions. Is the graph steeper at point C or at point E?

Find the slope of the tangent to the graph of f (x) at any point. estimate to the nearest tenth

Given the statement: The company lost $15,000 during the past 5 months. Choose the sentence that best expresses how rapidly, on average, the quantity has changed over the given interval.

A graph of a model for the sales of services between 2004 and 2008 by Kelly Services, Inc., a leading global provider of staffing services, is shown below. Use the graph to calculate the average rate of change in Kelly's sales of services between 2005 and 2007.

Find the derivative of the given function using the algebraic method.

If find .

Suppose the function G(t) represents a test grade (out of 100 points) as a function of hours studied. If points, approximate, to one decimal place, the slope of the tangent line when .

The function P gives the profit in dollars that a fraternity makes selling x T-shirts. Is it possible for to be negative? Explain.

The percentage of students meeting national mathematics benchmarks on the ACT increased from 39% in 2001 to 42% in 2010. Calculate the average rate of change. Round your answer to two decimal places.

An object is dropped off a building. Ignoring air resistance we know from physics that its height above ground t seconds after being dropped is given by Height feet. Determine the object's velocity after 2.5 seconds.

The function g gives the fuel efficiency, in miles per gallon, of a car traveling v miles per hour. Write a sentence of interpretation for the following statement. .

The function D gives the time, in years, that it takes for an investment to double if interest is continuously compounded at r%. Write a sentence of interpretation for

If find .

Ingredients of Change: Functions an Limits

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

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Exam 2: Describing Change: Rates

Determine whether the function is continuous or differentiable for given input values.

The function D gives the time, in years, that it takes for an investment to double if interest is continuously compounded at r%. Write a sentence of interpretation for

An Airline industry posted a profit of $17.8 million at the end of 2009 compared with a loss of $121.7 million in 2008. Calculate change.

At the indicated x-value, find the slope of the tangent line.

Calculate the average rate of change in disposable personal income between 1995 and 2000. Round your answer to the nearest dollar.

Use the figure to answer the questions. Is the graph steeper at point C or at point E?

Find the slope of the tangent to the graph of f (x) at any point. estimate to the nearest tenth

Given the statement: The company lost $15,000 during the past 5 months. Choose the sentence that best expresses how rapidly, on average, the quantity has changed over the given interval.

A graph of a model for the sales of services between 2004 and 2008 by Kelly Services, Inc., a leading global provider of staffing services, is shown below. Use the graph to calculate the average rate of change in Kelly's sales of services between 2005 and 2007.

Find the derivative of the given function using the algebraic method.

If find .

Suppose the function G(t) represents a test grade (out of 100 points) as a function of hours studied. If points, approximate, to one decimal place, the slope of the tangent line when .

The function P gives the profit in dollars that a fraternity makes selling x T-shirts. Is it possible for to be negative? Explain.

The percentage of students meeting national mathematics benchmarks on the ACT increased from 39% in 2001 to 42% in 2010. Calculate the average rate of change. Round your answer to two decimal places.

An object is dropped off a building. Ignoring air resistance we know from physics that its height above ground t seconds after being dropped is given by Height feet. Determine the object's velocity after 2.5 seconds.

The function g gives the fuel efficiency, in miles per gallon, of a car traveling v miles per hour. Write a sentence of interpretation for the following statement. .

The function D gives the time, in years, that it takes for an investment to double if interest is continuously compounded at r%. Write a sentence of interpretation for

If find .

Ingredients of Change: Functions an Limits

Determining Change: Derivatives

Analyzing Change: Applications of Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters