Question 1

Use the curve-sketching guideline, to select the graph of the function. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
A)  ​   
B)  ​   
C)  ​

Question 2

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent. ​

Accepted Answer

A)  $10,959.77 
B)  $10,870.79 
C)  $10,978.19 
D)  $10,923.56 
A)  $10,959.77 
B)  $10,870.79 
C)  $10,978.19 
D)  $10,923.56

Question 3

Evaluate the expression.
​   __________

Accepted Answer

The answer of Evaluate the expression.
​   __________...

Question 4

Use logarithms to solve the equation for t. Please round the answer to four decimal places.
​   ​
t = __________

Accepted Answer

The answer of Use logarithms to solve the equation for...

Question 5

Determine the intervals where the function   is decreasing. ​

Accepted Answer

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

Question 6

Use the facts that   and   to find the value of the logarithm. Round your answer to four decimal places.

Accepted Answer

The answer of Use the facts that   and...

Question 7

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 8

The Estradas are planning to buy a house 4 year(s) from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 8% / year during that 4-year period. If this economic prediction holds true, how much can they expect to pay for a house that currently costs $40,000? Round your answer to the nearest cent.
​
$__________

Accepted Answer

The answer of The Estradas are planning to buy a...

Question 9

Find the present value of $54,049 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest integer. ​

Accepted Answer

A)  $38,536 
B)  $38,089 
C)  $38,088 
D)  $38,316 
A)  $38,536 
B)  $38,089 
C)  $38,088 
D)  $38,316

Question 10

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 11

Use logarithms to solve the equation for t. Round your answer to four decimal places.
​   ​
t = __________

Accepted Answer

The answer of Use logarithms to solve the equation for...

Question 12

Online retail sales stood at $23.5 billion for 2000. For the next 2 years, they grew by 32.8% and 27.7% per year, respectively. For the next 6 years, online retail sales are projected to grow at 30.5%, 19.3%, 24.4%, 13.8%, 17.8%, and 10.3% per year, respectively. What are the projected online sales for 2008? Round your answer to the nearest tenth.
​
$__________ billion

Accepted Answer

The answer of Online retail sales stood at $23.5 billion...

Question 13

Suppose a radioactive substance decays according to the formula   . How long will it take for the substance to decay to half the original amount? ​

Accepted Answer

A)  It will take 5,166 years for the substance to decay to half the original amount. 
B)  It will take 5,277 years for the substance to decay to half the original amount. 
C)  It will take 40 years for the substance to decay to half the original amount. 
D)  It will take 5,622 years for the substance to decay to half the original amount. 
A)  It will take 5,166 years for the substance to decay to half the original amount. 
B)  It will take 5,277 years for the substance to decay to half the original amount. 
C)  It will take 40 years for the substance to decay to half the original amount. 
D)  It will take 5,622 years for the substance to decay to half the original amount.

Question 14

The length (in centimeters) of a typical Pacific halibut t years old is approximately ​   .
​
What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
​

Accepted Answer

A)  85.8 cm; 14.5 cm/yr; 202 cm; 
B)  115.6 cm; 13.8 cm/yr; 202 cm; 
C)  128.7 cm; 0.952 cm/yr; 229 cm; 
D)  202.0 cm; 11.7 cm/yr; 256 cm; 
A)  85.8 cm; 14.5 cm/yr; 202 cm; 
B)  115.6 cm; 13.8 cm/yr; 202 cm; 
C)  128.7 cm; 0.952 cm/yr; 229 cm; 
D)  202.0 cm; 11.7 cm/yr; 256 cm;

Question 15

Use the definition of a logarithm to prove   .

Accepted Answer

By the def

Question 16

The height (in feet) of a certain kind of tree is approximated by   where t is the age of the tree in years. Estimate the age of a 70-ft tree. Round your answer to the nearest hundredth.
​
__________ years

Accepted Answer

The answer of The height (in feet) of a certain...

Question 17

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 18

Evaluate the expression. ​   ​

Accepted Answer

A)  81 
B)  12 
C)  9 
D)  8 
A)  81 
B)  12 
C)  9 
D)  8

Question 19

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 20

Find the second derivative of the function.
​

Accepted Answer

The answer of Find the second derivative of the function.
​...

Use the curve-sketching guideline, to select the graph of the function.

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent.

Evaluate the expression. __________

Use logarithms to solve the equation for t. Please round the answer to four decimal places. t = __________

Determine the intervals where the function is decreasing.

Use the facts that and to find the value of the logarithm. Round your answer to four decimal places.

Find the derivative of the function.

Find the present value of $54,049 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest integer.

Find the derivative of the function.

Use logarithms to solve the equation for t. Round your answer to four decimal places. t = __________

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?

The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?

Use the definition of a logarithm to prove .

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Round your answer to the nearest hundredth. __________ years

Find the derivative of the function.

Evaluate the expression.

Find the derivative of the function.

Find the second derivative of the function.

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Exam 5: Exponential and Logarithmic Functions

Use the curve-sketching guideline, to select the graph of the function. ​ ​

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent. ​

Evaluate the expression. ​ __________

Use logarithms to solve the equation for t. Please round the answer to four decimal places. ​ ​ t = __________

Determine the intervals where the function is decreasing. ​

Use the facts that and to find the value of the logarithm. Round your answer to four decimal places.

Find the derivative of the function. ​

Find the present value of $54,049 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest integer. ​

Find the derivative of the function. ​ ​

Use logarithms to solve the equation for t. Round your answer to four decimal places. ​ ​ t = __________

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount? ​

The length (in centimeters) of a typical Pacific halibut t years old is approximately ​ . ​ What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? ​

Use the definition of a logarithm to prove .

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Round your answer to the nearest hundredth. ​ __________ years

Find the derivative of the function. ​ ​

Evaluate the expression. ​ ​

Find the derivative of the function. ​

Find the second derivative of the function. ​

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Use the curve-sketching guideline, to select the graph of the function.

Find the accumulated amount after 5 year(s) if $7,000 is invested at 9% compounded continuously. Round your answer to the nearest cent.

Evaluate the expression. __________

Use logarithms to solve the equation for t. Please round the answer to four decimal places. t = __________

Determine the intervals where the function is decreasing.

Find the derivative of the function.

Find the present value of $54,049 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest integer.

Find the derivative of the function.

Use logarithms to solve the equation for t. Round your answer to four decimal places. t = __________

Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?

The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?

The height (in feet) of a certain kind of tree is approximated by where t is the age of the tree in years. Estimate the age of a 70-ft tree. Round your answer to the nearest hundredth. __________ years

Find the derivative of the function.

Evaluate the expression.

Find the derivative of the function.

Find the second derivative of the function.