Question 1

​Determine whether the function below has any horizontal asymptotes. ​   ​

Accepted Answer

A)  ​horizontal asymptotes:   
B)  ​no horizontal asymptotes 
C)  ​horizontal asymptotes:   
D)  ​horizontal asymptotes:   
E)  ​​horizontal asymptotes:   
A)  ​horizontal asymptotes:   
B)  ​no horizontal asymptotes 
C)  ​horizontal asymptotes:   
D)  ​horizontal asymptotes:   
E)  ​​horizontal asymptotes:

Question 2

Determine the continuity of the function below. ​   ​​

Accepted Answer

A)  ​discontinuous at   
B)  ​continuous on the entire real number line 
C)  ​discontinuous at   
D)  ​discontinuous at   
E)  ​discontinuous at   
A)  ​discontinuous at   
B)  ​continuous on the entire real number line 
C)  ​discontinuous at   
D)  ​discontinuous at   
E)  ​discontinuous at

Question 3

Solve the following equation for x accurate to three decimal places. ​   ​

Accepted Answer

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

Question 4

​Find   if

Accepted Answer

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

Question 5

​Find   ,if   ​

Accepted Answer

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

Question 6

​The average typing speed N (in words per minute)after t weeks of lessons is modeled by   Find the rate at which the typing speed is changing when   weeks.Round your answer to two decimal places. ​

Accepted Answer

A)  ​1.51 words/min/week 
B)  ​2.15 words/min/week 
C)  ​2.51 words/min/week 
D)  ​4.38 words/min/week 
E)  ​5.04 words/min/week 
A)  ​1.51 words/min/week 
B)  ​2.15 words/min/week 
C)  ​2.51 words/min/week 
D)  ​4.38 words/min/week 
E)  ​5.04 words/min/week

Question 7

​Use the properties of logarithms to approximate   ,given that   ​

Accepted Answer

A)  ​-4.9767 
B)  ​-1.7579 
C)  ​0.4780 
D)  ​5.4195 
E)  ​4.9767 
A)  ​-4.9767 
B)  ​-1.7579 
C)  ​0.4780 
D)  ​5.4195 
E)  ​4.9767

Question 8

To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.

Accepted Answer

A)  $3,240.96 
B)  $3,260.41 
C)  $3,186.49 
D)  $2,926.00 
E)  $16,475.16 
A)  $3,240.96 
B)  $3,260.41 
C)  $3,186.49 
D)  $2,926.00 
E)  $16,475.16

Question 9

​Use the properties of logarithms to expand

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 10

​Find   ,if   ​

Accepted Answer

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

Question 11

​Find   ​   ​

Accepted Answer

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

Question 12

​Use implicit differentiation to find   ​   ​

Accepted Answer

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

Question 13

​Find the derivative of the function

Accepted Answer

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

Question 14

Assume the population P (in millions)of the United States from 1992 through 2005 can be modeled by the exponential function   ,where t is the time in years,with   corresponding to 1992.Use the model to estimate the population in the year 2009.Round your answer to the nearest million.

Accepted Answer

A)  5,973 million 
B)  958 million 
C)  1,336 million 
D)  353 million 
E)  5,972 million 
A)  5,973 million 
B)  958 million 
C)  1,336 million 
D)  353 million 
E)  5,972 million

Question 15

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 16

​The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by   During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years? ​

Accepted Answer

A)  ​The saturation point for the market is 3,000 units and 17,944 units will be sold after 5 years. 
B)  ​The saturation point for the market is 30,000 units and 26,049 units will be sold after 5 years. 
C)  ​The saturation point for the market is 30,000 units and 17,944 units will be sold after 5 years. 
D)  ​The saturation point for the market is 30,000 units and 18,067 units will be sold after 5 years. 
E)  ​The saturation point for the market is 3,000 units and 26,049 units will be sold after 5 years. 
A)  ​The saturation point for the market is 3,000 units and 17,944 units will be sold after 5 years. 
B)  ​The saturation point for the market is 30,000 units and 26,049 units will be sold after 5 years. 
C)  ​The saturation point for the market is 30,000 units and 17,944 units will be sold after 5 years. 
D)  ​The saturation point for the market is 30,000 units and 18,067 units will be sold after 5 years. 
E)  ​The saturation point for the market is 3,000 units and 26,049 units will be sold after 5 years.

Question 17

Solve the following equation for accurate to three decimal places. ​   ​

Accepted Answer

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

Question 18

​Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​does not exist 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​does not exist

Question 19

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. ​   ​

Accepted Answer

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

Question 20

​Locate any relative extrema and inflection points of the function   Use a graphing utility to confirm your results. ​

Accepted Answer

A)  ​relative maximum value   at   ; inflection point at   
B)  ​​relative minimum value   at   ; inflection point at   
C)  ​​​relative minimum value   at   ; no inflection points 
D)  ​relative minimum value   at   ; no inflection points 
E)  ​​relative maximum value   at   ; no inflection points 
A)  ​relative maximum value   at   ; inflection point at   
B)  ​​relative minimum value   at   ; inflection point at   
C)  ​​​relative minimum value   at   ; no inflection points 
D)  ​relative minimum value   at   ; no inflection points 
E)  ​​relative maximum value   at   ; no inflection points

Determine whether the function below has any horizontal asymptotes.

Determine the continuity of the function below.

Solve the following equation for x accurate to three decimal places.

Find if

Find ,if

The average typing speed N (in words per minute)after t weeks of lessons is modeled by Find the rate at which the typing speed is changing when weeks.Round your answer to two decimal places.

Use the properties of logarithms to approximate ,given that

To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.

Use the properties of logarithms to expand

Find ,if

Find

Use implicit differentiation to find

Find the derivative of the function

Assume the population P (in millions)of the United States from 1992 through 2005 can be modeled by the exponential function ,where t is the time in years,with corresponding to 1992.Use the model to estimate the population in the year 2009.Round your answer to the nearest million.

Find the derivative of the following function.

The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years?

Solve the following equation for accurate to three decimal places.

Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places.

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms.

Locate any relative extrema and inflection points of the function Use a graphing utility to confirm your results.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 4: Exponential and Logarithmic Functions

​Determine whether the function below has any horizontal asymptotes. ​ ​

Determine the continuity of the function below. ​ ​​

Solve the following equation for x accurate to three decimal places. ​ ​

​Find if

​Find ,if ​

​The average typing speed N (in words per minute)after t weeks of lessons is modeled by Find the rate at which the typing speed is changing when weeks.Round your answer to two decimal places. ​

​Use the properties of logarithms to approximate ,given that ​

To help their son buy a car on his 16th birthday,a boy's parents invest $1,900 on his 10th birthday.If the investment pays an annual rate of 9% compounded continuously,how much is available on his 16th birthday? Round your answer to the nearest cent.

​Use the properties of logarithms to expand

​Find ,if ​

​Find ​ ​

​Use implicit differentiation to find ​ ​

​Find the derivative of the function

Assume the population P (in millions)of the United States from 1992 through 2005 can be modeled by the exponential function ,where t is the time in years,with corresponding to 1992.Use the model to estimate the population in the year 2009.Round your answer to the nearest million.

​Find the derivative of the following function. ​ ​

​The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years? ​

Solve the following equation for accurate to three decimal places. ​ ​

​Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places. ​ ​

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. ​ ​

​Locate any relative extrema and inflection points of the function Use a graphing utility to confirm your results. ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Determine whether the function below has any horizontal asymptotes.

Determine the continuity of the function below.

Solve the following equation for x accurate to three decimal places.

Find if

Find ,if

The average typing speed N (in words per minute)after t weeks of lessons is modeled by Find the rate at which the typing speed is changing when weeks.Round your answer to two decimal places.

Use the properties of logarithms to approximate ,given that

Use the properties of logarithms to expand

Find ,if

Find

Use implicit differentiation to find

Find the derivative of the function

Find the derivative of the following function.

The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years?

Solve the following equation for accurate to three decimal places.

Find the relative maxima,and use a graphing utility to check your results.Round your answer to the two decimal places.

Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms.

Locate any relative extrema and inflection points of the function Use a graphing utility to confirm your results.