Question 1

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

Accepted Answer

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

Question 2

What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.

Accepted Answer

A)  $147,330.10 
B)  $18,292.68 
C)  $53,571.43 
D)  $24,961.93 
E)  $25,294.49 
A)  $147,330.10 
B)  $18,292.68 
C)  $53,571.43 
D)  $24,961.93 
E)  $25,294.49

Question 3

​Sketch the graph of the function   ​

Accepted Answer

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

Question 4

If   ,find   ​ ​

Accepted Answer

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

Question 5

Find   ​ ​   ​

Accepted Answer

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

Question 6

​Use a graphing utility to graph the function

Accepted Answer

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

Question 7

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

Accepted Answer

A)  ​-2.993 
B)  ​-0.100 
C)  ​2.182 
D)  ​-1.091 
E)  ​5.986 
A)  ​-2.993 
B)  ​-0.100 
C)  ​2.182 
D)  ​-1.091 
E)  ​5.986

Question 8

What is the annual percentage yield (or effective annual rate)for a nominal rate of 8.7% compounded quarterly? Round your answer to two decimal places.

Accepted Answer

A)  8.70% 
B)  9.06% 
C)  9.09% 
D)  8.99% 
E)  8.89% 
A)  8.70% 
B)  9.06% 
C)  9.09% 
D)  8.99% 
E)  8.89%

Question 9

Evaluate the expression   ​

Accepted Answer

A)  ​125 
B)  ​5 
C)  ​25 
D)  ​27 
E)  ​29 
A)  ​125 
B)  ​5 
C)  ​25 
D)  ​27 
E)  ​29

Question 10

​Find the second derivative of the function   ​

Accepted Answer

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

Question 11

​Use the properties of logarithms to write the expression as a single logarithm. ​   ​

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

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 14

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as   Find the derivative of the model. ​

Accepted Answer

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

Question 15

​Find the extrema of the function   by analyzing its graph below. ​
​   ​

Accepted Answer

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

Question 16

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 17

Write the logarithmic equation   as an exponential equation. ​

Accepted Answer

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

Question 18

Find   ​   ​

Accepted Answer

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

Question 19

The effective yield is the annual rate i that will produce the same interest per year as the nominal rate compounded n times per year.For a rate that is compounded n times per year,the formula for effective yield is given as   Find the effective yield for a nominal rate of 9%,compounded monthly.Round your answer to two decimal places. ​

Accepted Answer

A)  ​0.94% 
B)  ​9.62% 
C)  ​10.01% 
D)  ​1.50% 
E)  ​9.38% 
A)  ​0.94% 
B)  ​9.62% 
C)  ​10.01% 
D)  ​1.50% 
E)  ​9.38%

Question 20

​After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth   of its value for the previous year.Find a model for V(t),the value of the car after t years.

Accepted Answer

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

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

What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.

Sketch the graph of the function

If ,find

Find

Use a graphing utility to graph the function

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

What is the annual percentage yield (or effective annual rate)for a nominal rate of 8.7% compounded quarterly? Round your answer to two decimal places.

Evaluate the expression

Find the second derivative of the function

Use the properties of logarithms to write the expression as a single logarithm.

Find the derivative of the following function.

Find the derivative of the following function.

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model.

Find the extrema of the function by analyzing its graph below.

Find the derivative of the following function.

Write the logarithmic equation as an exponential equation.

Find

After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth of its value for the previous year.Find a model for V(t),the value of the car after t years.

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

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

What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.

​Sketch the graph of the function ​

If ,find ​ ​

Find ​ ​ ​

​Use a graphing utility to graph the function

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

What is the annual percentage yield (or effective annual rate)for a nominal rate of 8.7% compounded quarterly? Round your answer to two decimal places.

Evaluate the expression ​

​Find the second derivative of the function ​

​Use the properties of logarithms to write the expression as a single logarithm. ​ ​

​Find the derivative of the following function. ​ ​

​Find the derivative of the following function. ​ ​

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​

​Find the extrema of the function by analyzing its graph below. ​ ​ ​

​Find the derivative of the following function. ​ ​

Write the logarithmic equation as an exponential equation. ​

Find ​ ​

​After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth of its value for the previous year.Find a model for V(t),the value of the car after t years.

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

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

Sketch the graph of the function

If ,find

Find

Use a graphing utility to graph the function

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

Evaluate the expression

Find the second derivative of the function

Use the properties of logarithms to write the expression as a single logarithm.

Find the derivative of the following function.

Find the derivative of the following function.

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model.

Find the extrema of the function by analyzing its graph below.

Find the derivative of the following function.

Write the logarithmic equation as an exponential equation.

Find

After t years,the value of a car that originally cost $18,000 depreciates so that each year it is worth of its value for the previous year.Find a model for V(t),the value of the car after t years.