Question 1

Find the derivative of the function.

Accepted Answer

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

Question 2

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by   . Find the equilibrium price of the commodity.
(Hint: It's given by   . Also, use the fact that   .)

Accepted Answer

A)  The equilibrium price of the commodity is $7. 
B)  The equilibrium price of the commodity is $12. 
C)  The equilibrium price of the commodity is $9. 
D)  The equilibrium price of the commodity is $4. 
A)  The equilibrium price of the commodity is $7. 
B)  The equilibrium price of the commodity is $12. 
C)  The equilibrium price of the commodity is $9. 
D)  The equilibrium price of the commodity is $4.

Question 3

A women's clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by   dollars. Find to the nearest integer the rate of change of sales volume when t = 4.

Accepted Answer

A)  The rate of change of sales volume is - $3,028 per day. 
B)  The rate of change of sales volume is - $1,202 per day. 
C)  The rate of change of sales volume is - $1,211 per day. 
D)  The rate of change of sales volume is - $2 per day. 
A)  The rate of change of sales volume is - $3,028 per day. 
B)  The rate of change of sales volume is - $1,202 per day. 
C)  The rate of change of sales volume is - $1,211 per day. 
D)  The rate of change of sales volume is - $2 per day.

Question 4

Find the derivative of the function.

Accepted Answer

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

Question 5

Find the interest rate needed for an investment of $5,000 to grow to an amount of $7,000 in 4 year(s) if interest is compounded continuously.

Accepted Answer

A)  8.55% per year 
B)  8.41% per year 
C)  8.48% per year 
D)  8.62% per year 
E)  8.69% per year 
A)  8.55% per year 
B)  8.41% per year 
C)  8.48% per year 
D)  8.62% per year 
E)  8.69% per year

Question 6

Find the derivative of the function.

Accepted Answer

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

Question 7

Sketch the graphs of the functions on the same axes.

Accepted Answer

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

Question 8

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. 8% / year compounded monthly   _____%
8% / year compounded daily   _____%

Accepted Answer

A)  8.328%, 8.243% 
B)  8.243%, 8.000% 
C)  8.328%, 8.000% 
D)  8.300%, 8.328% 
A)  8.328%, 8.243% 
B)  8.243%, 8.000% 
C)  8.328%, 8.000% 
D)  8.300%, 8.328%

Question 9

Use logarithms to solve the equation for t.

Accepted Answer

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

Question 10

Find the derivative of the function.

Accepted Answer

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

Question 11

The concentration of a drug in an organ at any time t (in seconds) is given by   where C(t) is measured in milligrams/cubic centimeter   . What is the concentration to four decimal places of the drug in the organ after 15 sec?

Accepted Answer

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

Question 12

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

The answer of Use logarithmic differentiation to find the derivative...

Question 13

Simplify the expression.

Accepted Answer

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

Question 14

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by   . How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?

Accepted Answer

A)  13 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 883 children eventually contracted the disease 
B)  10 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 1,200 children eventually contracted the disease 
C)  13 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,200 children eventually contracted the disease 
D)  15 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,354 children eventually contracted the disease 
A)  13 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 883 children eventually contracted the disease 
B)  10 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 1,200 children eventually contracted the disease 
C)  13 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,200 children eventually contracted the disease 
D)  15 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,354 children eventually contracted the disease

Question 15

Find the derivative of the function.

Accepted Answer

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

Question 16

Solve the equation for x.

Accepted Answer

The answer of Solve the equation for x.  ...

Question 17

Use the laws of logarithms to simplify the expression.

Accepted Answer

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

Question 18

Solve the equation for x.     __________

Accepted Answer

The answer of Solve the equation for x.  ...

Find the derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .)

A women's clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by dollars. Find to the nearest integer the rate of change of sales volume when t = 4.

Find the derivative of the function.

Find the interest rate needed for an investment of $5,000 to grow to an amount of $7,000 in 4 year(s) if interest is compounded continuously.

Find the derivative of the function.

Sketch the graphs of the functions on the same axes.

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. 8% / year compounded monthly _% 8% / year compounded daily _%

Use logarithms to solve the equation for t.

Find the derivative of the function.

The concentration of a drug in an organ at any time t (in seconds) is given by where C(t) is measured in milligrams/cubic centimeter . What is the concentration to four decimal places of the drug in the organ after 15 sec?

Use logarithmic differentiation to find the derivative of the function.

Simplify the expression.

Find the derivative of the function.

Solve the equation for x.

Use the laws of logarithms to simplify the expression.

Solve the equation for x. __________

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 5: Exponential and Logarithmic Functions

Find the derivative of the function.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by . Find the equilibrium price of the commodity. (Hint: It's given by . Also, use the fact that .)

A women's clothing chain store, found that t days after the end of a sales promotion the volume of sales was given by dollars. Find to the nearest integer the rate of change of sales volume when t = 4.

Find the derivative of the function.

Find the interest rate needed for an investment of $5,000 to grow to an amount of $7,000 in 4 year(s) if interest is compounded continuously.

Find the derivative of the function.

Sketch the graphs of the functions on the same axes.

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. 8% / year compounded monthly _____% 8% / year compounded daily _____%

Use logarithms to solve the equation for t.

Find the derivative of the function.

The concentration of a drug in an organ at any time t (in seconds) is given by where C(t) is measured in milligrams/cubic centimeter . What is the concentration to four decimal places of the drug in the organ after 15 sec?

Use logarithmic differentiation to find the derivative of the function.

Simplify the expression.

Find the derivative of the function.

Solve the equation for x.

Use the laws of logarithms to simplify the expression.

Solve the equation for x. __________

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Find the effective rate corresponding to the given nominal rate. Round your answers to three decimal places. 8% / year compounded monthly _% 8% / year compounded daily _%