Question 1

Sketch the graphs of the given functions on the same axes. ​   and   ​

Accepted Answer

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

Question 2

The monthly demand for a certain brand of perfume is given by the demand equation   where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000. ​

Accepted Answer

A)  The rate of change of the price is -3.26 cents per bottle. 
B)  The rate of change of the price is -2.46 cents per bottle. 
C)  The rate of change of the price is 4.92 cents per bottle. 
D)  The rate of change of the price is -10.46 cents per bottle. 
A)  The rate of change of the price is -3.26 cents per bottle. 
B)  The rate of change of the price is -2.46 cents per bottle. 
C)  The rate of change of the price is 4.92 cents per bottle. 
D)  The rate of change of the price is -10.46 cents per bottle.

Question 3

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)  12 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,400 children eventually contracted the disease 
B)  15 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,083 children eventually contracted the disease 
C)  17 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,246 children eventually contracted the disease 
D)  15 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,400 children eventually contracted the disease 
A)  12 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,400 children eventually contracted the disease 
B)  15 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,083 children eventually contracted the disease 
C)  17 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,246 children eventually contracted the disease 
D)  15 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,400 children eventually contracted the disease

Question 4

Express the equation in logarithmic form.
​

Accepted Answer

The answer of Express the equation in logarithmic form.
​ ...

Question 5

A certain piece of machinery was purchased 2 year(s) ago by Garland Mills for $500,000. Its present resale value is $320,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now? ​

Accepted Answer

A)  The resale value of the machinery will be $204,800 
B)  The resale value of the machinery will be $205,911 
C)  The resale value of the machinery will be $204,789 
D)  The resale value of the machinery will be $204,911 
A)  The resale value of the machinery will be $204,800 
B)  The resale value of the machinery will be $205,911 
C)  The resale value of the machinery will be $204,789 
D)  The resale value of the machinery will be $204,911

Question 6

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 an 60-ft tree. Round your answer to the nearest hundredth. ​

Accepted Answer

A)  10.00 years 
B)  13.60 years 
C)  13.01 years 
D)  12.17 years 
A)  10.00 years 
B)  13.60 years 
C)  13.01 years 
D)  12.17 years

Question 7

Solve the equation for   . ​   ​

Accepted Answer

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

Question 8

Find the derivative of the function.
​

Accepted Answer

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

Question 9

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth.
​
__________%

Accepted Answer

The answer of Find the nominal interest rate that, when...

Question 10

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 11

Solve the equation for   . ​   ​

Accepted Answer

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

Question 12

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth.
​
__________%

Accepted Answer

The answer of A condominium complex was purchased by a...

Question 13

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by   . ​
Select the graph of this function. At what level is the demand expected to stabilize?
​

Accepted Answer

A)  ​   1,900 computers 
B)  ​   ​ 1,800 computers ​ 
C)  ​   2,100 computers ​ 
D)  ​   1,800 computers ​ 
E)  ​   1,900 computers 
A)  ​   1,900 computers 
B)  ​   ​ 1,800 computers ​ 
C)  ​   2,100 computers ​ 
D)  ​   1,800 computers ​ 
E)  ​   1,900 computers

Question 14

Eleni, who is now 55 years old, is employed by a firm that guarantees her a pension of $90,000/year at age 70. What is the present value of her first year's pension if inflation over the next 15 year(s) is at the given rate. Assume that inflation is continuously compounded. Round your answer to the nearest cent. ​
6% _________
​
9% _________
​
18% _________
​

Accepted Answer

A)  $64,219.68, $71,866.46, $6,048.50 
B)  $36,591.27, $23,331.62, $6,048.50 
C)  $57,386.53, $64,219.68, $6,048.50 
D)  $57,386.53, $64,219.68, $71,866.46 
A)  $64,219.68, $71,866.46, $6,048.50 
B)  $36,591.27, $23,331.62, $6,048.50 
C)  $57,386.53, $64,219.68, $6,048.50 
D)  $57,386.53, $64,219.68, $71,866.46

Question 15

A study on worldwide oil use was prepared for a major oil company. The study predicted that the amount of oil used to fuel productivity in a certain country is given by ​   ​
Where f (t) denotes the number of barrels per $1,000 of economic output and t is measured in decades (   corresponds to 1965). Compute f '(0) and f ​'(2).
​
Round the answer to the nearest hundredth.
​

Accepted Answer

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

Question 16

Use the laws of logarithms to simplify the expression.
​

Accepted Answer

The answer of Use the laws of logarithms to simplify...

Question 17

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place. ​

Accepted Answer

A)  8.9 year(s) 
B)  8.6 year(s) 
C)  8.4 year(s) 
D)  8.7 year(s) 
A)  8.9 year(s) 
B)  8.6 year(s) 
C)  8.4 year(s) 
D)  8.7 year(s)

Question 18

Find the derivative of the function.
​

Accepted Answer

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

Question 19

Find the derivative of the function.
​

Accepted Answer

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

Question 20

A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places. ​

Accepted Answer

A)  22.73% 
B)  23.17% 
C)  22.52% 
D)  23.84% 
A)  22.73% 
B)  23.17% 
C)  22.52% 
D)  23.84%

Sketch the graphs of the given functions on the same axes. and

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.

Express the equation in logarithmic form.

A certain piece of machinery was purchased 2 year(s) ago by Garland Mills for $500,000. Its present resale value is $320,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now?

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 an 60-ft tree. Round your answer to the nearest hundredth.

Solve the equation for .

Find the derivative of the function.

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth. __________%

Find the derivative of the function.

Solve the equation for .

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. __________%

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by . Select the graph of this function. At what level is the demand expected to stabilize?

Use the laws of logarithms to simplify the expression.

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place.

Find the derivative of the function.

Find the derivative of the function.

A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places.

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

Sketch the graphs of the given functions on the same axes. ​ and ​

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000. ​

Express the equation in logarithmic form. ​

A certain piece of machinery was purchased 2 year(s) ago by Garland Mills for $500,000. Its present resale value is $320,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now? ​

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 an 60-ft tree. Round your answer to the nearest hundredth. ​

Solve the equation for . ​ ​

Find the derivative of the function. ​

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth. ​ __________%

Find the derivative of the function. ​ ​

Solve the equation for . ​ ​

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. ​ __________%

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by . ​ Select the graph of this function. At what level is the demand expected to stabilize? ​

Use the laws of logarithms to simplify the expression. ​

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place. ​

Find the derivative of the function. ​

Find the derivative of the function. ​

A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places. ​

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

Sketch the graphs of the given functions on the same axes. and

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000.

Express the equation in logarithmic form.

A certain piece of machinery was purchased 2 year(s) ago by Garland Mills for $500,000. Its present resale value is $320,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now?

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 an 60-ft tree. Round your answer to the nearest hundredth.

Solve the equation for .

Find the derivative of the function.

Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of 20% / year. Round your answer to the nearest hundredth. __________%

Find the derivative of the function.

Solve the equation for .

A condominium complex was purchased by a group of private investors for $1.4 million and sold 4 year(s) later for $3.1 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to the nearest hundredth. __________%

Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by . Select the graph of this function. At what level is the demand expected to stabilize?

Use the laws of logarithms to simplify the expression.

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place.

Find the derivative of the function.

Find the derivative of the function.

A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places.