Question 1

​Find   ,if

Accepted Answer

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

Question 2

How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.

Accepted Answer

A)  $47.49 
B)  $93.15 
C)  $140.64 
D)  $2,924.71 
E)  $3,017.87 
A)  $47.49 
B)  $93.15 
C)  $140.64 
D)  $2,924.71 
E)  $3,017.87

Question 3

The management of a factory finds that the maximum number of units a worker can produce in a day is 30.The learning curve for the number of units N produced per day after a new employee has worked days is modeled by   After 20 days on the job,a worker is producing 19 units in a day.How many days should pass before this worker is producing 25 units per day? ​

Accepted Answer

A)  about 36 days. 
B)  about 45 days. 
C)  about 30 days. 
D)  about 10 days. 
A)  about 36 days. 
B)  about 45 days. 
C)  about 30 days. 
D)  about 10 days.

Question 4

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

Accepted Answer

A)  ​-0.219 
B)  ​2.033 
C)  ​0.274 
D)  ​-2.033 
E)  ​-0.224 
A)  ​-0.219 
B)  ​2.033 
C)  ​0.274 
D)  ​-2.033 
E)  ​-0.224

Question 5

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 6

​Simplify   ​

Accepted Answer

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

Question 7

The demand function for a product is modeled by   What is the limit of the price as x increases without bound?

Accepted Answer

A)  The limit of the price as x increases without bound is -1. 
B)  The limit of the price as x increases without bound is 1. 
C)  The limit of the price as x increases without bound is 0. 
D)  The limit of the price as x increases without bound is 3,000. 
E)  The limit of the price as x increases without bound is 4. 
A)  The limit of the price as x increases without bound is -1. 
B)  The limit of the price as x increases without bound is 1. 
C)  The limit of the price as x increases without bound is 0. 
D)  The limit of the price as x increases without bound is 3,000. 
E)  The limit of the price as x increases without bound is 4.

Question 8

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

Accepted Answer

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

Question 9

​The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer. ​

Accepted Answer

A)  ​10 bacteria 
B)  903 ​bacteria 
C)  ​1,008 bacteria 
D)  ​23 bacteria 
E)  ​18 bacteria 
A)  ​10 bacteria 
B)  903 ​bacteria 
C)  ​1,008 bacteria 
D)  ​23 bacteria 
E)  ​18 bacteria

Question 10

​How long (in years)would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places. ​

Accepted Answer

A)  ​2.95 years 
B)  ​2.70 years 
C)  ​0.56 years 
D)  3.38​ years 
E)  ​2.56 years 
A)  ​2.95 years 
B)  ​2.70 years 
C)  ​0.56 years 
D)  3.38​ years 
E)  ​2.56 years

Question 11

​Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 12

Use the properties of exponents to simplify the expression   ​

Accepted Answer

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

Question 13

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly. ​

Accepted Answer

A)  $9,072.00 
B)  $4,799.87 
C)  $7,043.82 
D)  $7,122.70 
E)  $7,164.22 
A)  $9,072.00 
B)  $4,799.87 
C)  $7,043.82 
D)  $7,122.70 
E)  $7,164.22

Question 14

​Find the second derivative of the function   ​

Accepted Answer

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

Question 15

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

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

​Solve for the equation for   ​

Accepted Answer

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

Question 18

​Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years   ,   Round your answer to the nearest cent. ​

Accepted Answer

A)  ​$49787.07 
B)  ​$50787.07 
C)  ​$49000.04 
D)  ​$40000.06 
A)  ​$49787.07 
B)  ​$50787.07 
C)  ​$49000.04 
D)  ​$40000.06

Question 19

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

Accepted Answer

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

Question 20

The cost of producing x units of a product is modeled by   Find the minimum average cost analytically.Round your answer to two decimal places. ​

Accepted Answer

A)  ​400.00 dollars per unit 
B)  ​381.19 dollars per unit 
C)  374.43​ dollars per unit 
D)  376.66​ dollars per unit 
E)  ​374.53 dollars per unit 
A)  ​400.00 dollars per unit 
B)  ​381.19 dollars per unit 
C)  374.43​ dollars per unit 
D)  376.66​ dollars per unit 
E)  ​374.53 dollars per unit

Find ,if

How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.

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

Find the derivative of the following function.

Simplify

The demand function for a product is modeled by What is the limit of the price as x increases without bound?

Locate any relative extrema and inflection points of the function

The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer.

How long (in years)would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places.

Find the derivative of the following function.

Use the properties of exponents to simplify the expression

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly.

Find the second derivative of the function

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

Sketch the graph of the function

Solve for the equation for

Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years , Round your answer to the nearest cent.

Write the expression as the logarithm of a single quantity.

The cost of producing x units of a product is modeled by Find the minimum average cost analytically.Round your answer to two decimal places.

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 ,if

How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.

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

​Find the derivative of the following function. ​ ​

​Simplify ​

The demand function for a product is modeled by What is the limit of the price as x increases without bound?

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

​The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer. ​

​How long (in years)would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places. ​

​Find the derivative of the following function. ​ ​

Use the properties of exponents to simplify the expression ​

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly. ​

​Find the second derivative of the function ​

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

Sketch the graph of the function ​

​Solve for the equation for ​

​Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years , Round your answer to the nearest cent. ​

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

The cost of producing x units of a product is modeled by Find the minimum average cost analytically.Round your answer to two decimal places. ​

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 ,if

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

Find the derivative of the following function.

Simplify

Locate any relative extrema and inflection points of the function

The number of a certain type of bacteria increases continuously at a rate proportional to the number present.There are 100 present initially,and 200 present 6 hours later.How many will there be 20 hours after the initial time? Round your answer to the nearest integer.

How long (in years)would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places.

Find the derivative of the following function.

Use the properties of exponents to simplify the expression

Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly.

Find the second derivative of the function

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

Sketch the graph of the function

Solve for the equation for

Determine the principal P that must be invested at interest rate r compounded continuously,so that $1,000,000 will be available for retirement in years , Round your answer to the nearest cent.

Write the expression as the logarithm of a single quantity.

The cost of producing x units of a product is modeled by Find the minimum average cost analytically.Round your answer to two decimal places.