Question 1

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 2

​If   ,find

Accepted Answer

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

Question 3

​The demand function for a product is modeled by   Find the price of the product if the quantity demanded is   Round your answer to two decimal places where applicable.

Accepted Answer

A)  ​$158.51 
B)  ​$2,468.78 
C)  ​$531.22 
D)  ​$2,478.98 
E)  ​$541.52 
A)  ​$158.51 
B)  ​$2,468.78 
C)  ​$531.22 
D)  ​$2,478.98 
E)  ​$541.52

Question 4

​Find the extrema of the function   ​

Accepted Answer

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

Question 5

​What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

Accepted Answer

A)  ​$4,632.79 
B)  ​$4,687.00 
C)  ​$6,075.00 
D)  ​$6,379.31 
E)  ​$8,258.80 
A)  ​$4,632.79 
B)  ​$4,687.00 
C)  ​$6,075.00 
D)  ​$6,379.31 
E)  ​$8,258.80

Question 6

​Write the expression   as the logarithm of a single quantity.

Accepted Answer

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

Question 7

​Future value.The future value that accrues when $700 is invested at 9%,compounded continuously,is   ,where t is the number of years.At what rate is the money in this account growing when   ?

Accepted Answer

A)  ​$10.03 per year 
B)  $65.57 per year​ 
C)  ​$1,003.33 per year 
D)  ​$725.66 per year 
E)  ​$90.30 per year 
A)  ​$10.03 per year 
B)  $65.57 per year​ 
C)  ​$1,003.33 per year 
D)  ​$725.66 per year 
E)  ​$90.30 per year

Question 8

​Find an equation of the tangent line to the graph of   at the point   ​

Accepted Answer

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

Question 9

​If   ,find   ​

Accepted Answer

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

Question 10

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 11

​Sketch the graph of the function   ​

Accepted Answer

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

Question 12

​Find   ​   ​

Accepted Answer

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

Question 13

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 14

​Find the derivative of   ​

Accepted Answer

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

Question 15

​What percent of a present amount of radioactive radium   will remain after 900 years? The half-life of radium is 1,600 years. ​

Accepted Answer

A)  ​45% 
B)  ​25% 
C)  ​65% 
D)  ​68% 
A)  ​45% 
B)  ​25% 
C)  ​65% 
D)  ​68%

Question 16

​Write the equation of the line tangent to the graph of   ​

Accepted Answer

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

Question 17

​Write the exponential equation   as a logarithmic equation.

Accepted Answer

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

Question 18

​Write the following expression as a logarithm of a single quantity. ​   ​

Accepted Answer

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

Question 19

After t years,the remaining mass y(in grams)of 16 grams of a radioactive element whose half-life is 34 years is given by   ,for   How much of the initial mass remains after 136 years? Round your answer to two decimal places. ​

Accepted Answer

A)  ​2.00 grams 
B)  ​2.20 grams 
C)  ​3.30 grams 
D)  ​2.90 grams 
E)  ​1.00 gram 
A)  ​2.00 grams 
B)  ​2.20 grams 
C)  ​3.30 grams 
D)  ​2.90 grams 
E)  ​1.00 gram

Question 20

​Use the properties of logarithms to expand   ​

Accepted Answer

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

Find the derivative of the following function.

If ,find

The demand function for a product is modeled by Find the price of the product if the quantity demanded is Round your answer to two decimal places where applicable.

Find the extrema of the function

What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

Write the expression as the logarithm of a single quantity.

Future value.The future value that accrues when $700 is invested at 9%,compounded continuously,is ,where t is the number of years.At what rate is the money in this account growing when ?

Find an equation of the tangent line to the graph of at the point

If ,find

Find the derivative of the following function.

Sketch the graph of the function

Find

Find the derivative of the following function.

Find the derivative of

What percent of a present amount of radioactive radium will remain after 900 years? The half-life of radium is 1,600 years.

Write the equation of the line tangent to the graph of

Write the exponential equation as a logarithmic equation.

Write the following expression as a logarithm of a single quantity.

After t years,the remaining mass y(in grams)of 16 grams of a radioactive element whose half-life is 34 years is given by ,for How much of the initial mass remains after 136 years? Round your answer to two decimal places.

Use the properties of logarithms to expand

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 derivative of the following function. ​ ​

​If ,find

​The demand function for a product is modeled by Find the price of the product if the quantity demanded is Round your answer to two decimal places where applicable.

​Find the extrema of the function ​

​What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

​Write the expression as the logarithm of a single quantity.

​Future value.The future value that accrues when $700 is invested at 9%,compounded continuously,is ,where t is the number of years.At what rate is the money in this account growing when ?

​Find an equation of the tangent line to the graph of at the point ​

​If ,find ​

​Find the derivative of the following function. ​ ​

​Sketch the graph of the function ​

​Find ​ ​

Find the derivative of the following function. ​ ​

​Find the derivative of ​

​What percent of a present amount of radioactive radium will remain after 900 years? The half-life of radium is 1,600 years. ​

​Write the equation of the line tangent to the graph of ​

​Write the exponential equation as a logarithmic equation.

​Write the following expression as a logarithm of a single quantity. ​ ​

After t years,the remaining mass y(in grams)of 16 grams of a radioactive element whose half-life is 34 years is given by ,for How much of the initial mass remains after 136 years? Round your answer to two decimal places. ​

​Use the properties of logarithms to expand ​

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 derivative of the following function.

If ,find

The demand function for a product is modeled by Find the price of the product if the quantity demanded is Round your answer to two decimal places where applicable.

Find the extrema of the function

What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?

Write the expression as the logarithm of a single quantity.

Future value.The future value that accrues when $700 is invested at 9%,compounded continuously,is ,where t is the number of years.At what rate is the money in this account growing when ?

Find an equation of the tangent line to the graph of at the point

If ,find

Find the derivative of the following function.

Sketch the graph of the function

Find

Find the derivative of the following function.

Find the derivative of

What percent of a present amount of radioactive radium will remain after 900 years? The half-life of radium is 1,600 years.

Write the equation of the line tangent to the graph of

Write the exponential equation as a logarithmic equation.

Write the following expression as a logarithm of a single quantity.

After t years,the remaining mass y(in grams)of 16 grams of a radioactive element whose half-life is 34 years is given by ,for How much of the initial mass remains after 136 years? Round your answer to two decimal places.

Use the properties of logarithms to expand