Question 1

Find the exponential function   that passes through the two given points (0,7)and (6,8).

Accepted Answer

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

Question 2

​Find the y-value at the relative minima,and use a graphing utility to check your result. ​   ​

Accepted Answer

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

Question 3

​Find an equation of the tangent line to the graph of   at the point (64,3). ​

Accepted Answer

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

Question 4

​Carbon-14 (14C)dating assumes that the carbon on the Earth today has the same radioactive content as it did centuries ago.If this is true,then the amount of 14C absorbed by a tree that grew several centuries ago should be the same as the amount of 14C absorbed by a similar tree today.A piece of ancient charcoal contains only 24% as much of the radioactive carbon as a piece of modern charcoal.How long ago was the tree burned to make the ancient charcoal? (The half-life of 14C is 5715 years.)Round your answer to the nearest integer. ​

Accepted Answer

A)  ​2,776 years 
B)  ​30,751 years 
C)  ​2,781 years 
D)  ​11,767 years 
E)  ​11,772 years 
A)  ​2,776 years 
B)  ​30,751 years 
C)  ​2,781 years 
D)  ​11,767 years 
E)  ​11,772 years

Question 5

​Find   ,if   ​

Accepted Answer

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

Question 6

Solve the exponential equation.Give answers correct to 3 decimal places. ​   ​

Accepted Answer

A)  343 
B)  0.571 
C)  0.712 
D)  0.356 
E)  0.805 
A)  343 
B)  0.571 
C)  0.712 
D)  0.356 
E)  0.805

Question 7

Sketch the graph of the function   ​

Accepted Answer

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

Question 8

​Find   ,if   ​

Accepted Answer

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

Question 9

​Find the derivative of

Accepted Answer

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

Question 10

​Locate any relative extrema and inflection points of the function   ​

Accepted Answer

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

Question 11

​Find   ,if   ​

Accepted Answer

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

Question 12

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 13

​With an annual rate of inflation of 4% over the next 10 years,the approximate cost of goods or services during any year in the decade is given by   where t is the time (in years)and P is the present cost.The price of an oil change for a car is presently $24.95.Estimate the price 10 years from now.Round your answer to the nearest cent.

Accepted Answer

A)  ​​$37.09 
B)  ​$36.93 
C)  ​​$89.00 
D)  ​​$63.90 
A)  ​​$37.09 
B)  ​$36.93 
C)  ​​$89.00 
D)  ​​$63.90

Question 14

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 15

​Find the derivative of the function   ​

Accepted Answer

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

Question 16

​Sketch the graph of the function   ​

Accepted Answer

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

Question 17

​Use a graphing utility to graph the function   Be sure to choose an appropriate viewing window. ​

Accepted Answer

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

Question 18

​Use the properties of logarithms to write the expression   as a sum,difference,or multiple of logarithms.

Accepted Answer

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

Question 19

​Find the relative minima,and use a graphing utility to check your results. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​0 
E)  ​does not exist 
A)  ​   
B)  ​   
C)  ​   
D)  ​0 
E)  ​does not exist

Question 20

​Find   ,if   ​

Accepted Answer

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

Find the exponential function that passes through the two given points (0,7)and (6,8).

Find the y-value at the relative minima,and use a graphing utility to check your result.

Find an equation of the tangent line to the graph of at the point (64,3).

Find ,if

Solve the exponential equation.Give answers correct to 3 decimal places.

Sketch the graph of the function

Find ,if

Find the derivative of

Locate any relative extrema and inflection points of the function

Find ,if

Find the derivative of the following function.

Find the derivative of the following function.

Find the derivative of the function

Sketch the graph of the function

Use a graphing utility to graph the function Be sure to choose an appropriate viewing window.

Use the properties of logarithms to write the expression as a sum,difference,or multiple of logarithms.

Find the relative minima,and use a graphing utility to check your results.

Find ,if

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

Find the exponential function that passes through the two given points (0,7)and (6,8).

​Find the y-value at the relative minima,and use a graphing utility to check your result. ​ ​

​Find an equation of the tangent line to the graph of at the point (64,3). ​

​Find ,if ​

Solve the exponential equation.Give answers correct to 3 decimal places. ​ ​

Sketch the graph of the function ​

​Find ,if ​

​Find the derivative of

​Locate any relative extrema and inflection points of the function ​

​Find ,if ​

​Find the derivative of the following function. ​ ​

​Find the derivative of the following function. ​ ​

​Find the derivative of the function ​

​Sketch the graph of the function ​

​Use a graphing utility to graph the function Be sure to choose an appropriate viewing window. ​

​Use the properties of logarithms to write the expression as a sum,difference,or multiple of logarithms.

​Find the relative minima,and use a graphing utility to check your results. ​ ​

​Find ,if ​

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

Find the y-value at the relative minima,and use a graphing utility to check your result.

Find an equation of the tangent line to the graph of at the point (64,3).

Find ,if

Solve the exponential equation.Give answers correct to 3 decimal places.

Sketch the graph of the function

Find ,if

Find the derivative of

Locate any relative extrema and inflection points of the function

Find ,if

Find the derivative of the following function.

Find the derivative of the following function.

Find the derivative of the function

Sketch the graph of the function

Use a graphing utility to graph the function Be sure to choose an appropriate viewing window.

Use the properties of logarithms to write the expression as a sum,difference,or multiple of logarithms.

Find the relative minima,and use a graphing utility to check your results.

Find ,if