Question 1

Graph the function. ​   ​

Accepted Answer

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

Question 2

Write the expression as the sum or difference of two logarithmic functions containing no exponents.

Accepted Answer

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

Question 3

Use a calculator to determine whether expression (a) is equivalent to expression (b). ​     ​

Accepted Answer

A) equivalent 
B) not equivalent 
A) equivalent 
B) not equivalent

Question 4

Graph the function   . ​

Accepted Answer

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

Question 5

Use the formula   to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $900 at interest rate 9% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places. ​

Accepted Answer

A) 2.60 years 
B) 15.58 years 
C) 3.89 years 
D) 4.02 years 
E) 7.79 years 
A) 2.60 years 
B) 15.58 years 
C) 3.89 years 
D) 4.02 years 
E) 7.79 years

Question 6

Solve for x by writing the equation in exponential form. ​   ​

Accepted Answer

A)    
B) ​   
C) 124 
D) 5 
E) 45 
A)    
B) ​   
C) 124 
D) 5 
E) 45

Question 7

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 8

The monthly sales S for a product is given by   , where x is the number of months that have passed since the end of a promotional campaign. How many months after the end of the campaign will sales drop below 6,000, if no new campaign is initiated? Round to two decimal places. ​

Accepted Answer

A) 2.65 months 
B) 4.01 months 
C) 4.97 months 
D) 6.17 months 
E) 7.38 months 
A) 2.65 months 
B) 4.01 months 
C) 4.97 months 
D) 6.17 months 
E) 7.38 months

Question 9

Use a calculator to evaluate the expression. Round your answer to two decimal places, if necessary. ​

Accepted Answer

A) 46,656 
B) 1 
C) 1.35 
D) 8.09 
E) 36 
A) 46,656 
B) 1 
C) 1.35 
D) 8.09 
E) 36

Question 10

If $4,000 is invested at an annual rate of 8% compounded continuously, the future value S at any time t (in years) is given by   . How long does it take for the investment to double? Round your answer to one decimal place. ​

Accepted Answer

A) 8.7years 
B) 6.9 years 
C) 7.9 years 
D) 10.2 years 
E) 11.3 years 
A) 8.7years 
B) 6.9 years 
C) 7.9 years 
D) 10.2 years 
E) 11.3 years

Question 11

Find an equivalent expression for the given logarithm using the change-of-base formula. ​   ​

Accepted Answer

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

Question 12

On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by   , where y is the total number infected at time t (in days). The school will shut down if 50% of the students are ill. What value of t corresponds to this percentage? ​

Accepted Answer

A) Infinity 
B) 8.19 
C) 9.30 
D) 6.44 
E) 3.96 
A) Infinity 
B) 8.19 
C) 9.30 
D) 6.44 
E) 3.96

Question 13

Graph the function. ​   ​

Accepted Answer

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

Question 14

Between the years 1960 and 2002, the percent of women in the work force is given by   , where x is the number of years past 1950 (Source: U.S. Bureau of Labor Statistics). Graph this function with a graphing utility and use the graph drawn to estimate the year in which the percent reached 60. Round your answer to the nearest year. ​

Accepted Answer

A) 1990 
B) 1997 
C) 2002 
D) 2010 
E) 2015 
A) 1990 
B) 1997 
C) 2002 
D) 2010 
E) 2015

Question 15

Express   in the form   with an appropriate value of   . ​

Accepted Answer

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

Question 16

Use a calculator to evaluate the expression. Round your answer to six decimal places. ​   ​

Accepted Answer

A) -0.125000 
B) -8.000000 
C) -6.000000 
D) 5.062500 
E) 0.125000 
A) -0.125000 
B) -8.000000 
C) -6.000000 
D) 5.062500 
E) 0.125000

Question 17

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 18

Use properties of logarithms or a definition to simplify the expression. ​
If   find   .
​

Accepted Answer

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

Question 19

The following table gives the average number of students per computer in public schools for the school years that ended in 1985 through 2002. Find an exponential model for these data. How many students per computer in public schools does this model predict for 2005?​ Round your answer to two decimal places. ​​​   ​
Source: Quality Education Data, Inc., Denver, Colorado​
​​

Accepted Answer

A) ​1.92 
B) ​2.42 
C) ​4.32 
D) ​3.42 
E) ​4.92 
A) ​1.92 
B) ​2.42 
C) ​4.32 
D) ​3.42 
E) ​4.92

Question 20

Use properties of logarithms or a definition to simplify the expression. ​
If   , find   .
​

Accepted Answer

A) 5 
B) 10 
C)    
D) 100,000 
E) 50 
A) 5 
B) 10 
C)    
D) 100,000 
E) 50

Graph the function.

Write the expression as the sum or difference of two logarithmic functions containing no exponents.

Use a calculator to determine whether expression (a) is equivalent to expression (b).

Graph the function .

Use the formula to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $900 at interest rate 9% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places.

Solve for x by writing the equation in exponential form.

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

The monthly sales S for a product is given by , where x is the number of months that have passed since the end of a promotional campaign. How many months after the end of the campaign will sales drop below 6,000, if no new campaign is initiated? Round to two decimal places.

Use a calculator to evaluate the expression. Round your answer to two decimal places, if necessary.

If $4,000 is invested at an annual rate of 8% compounded continuously, the future value S at any time t (in years) is given by . How long does it take for the investment to double? Round your answer to one decimal place.

Find an equivalent expression for the given logarithm using the change-of-base formula.

Graph the function.

Express in the form with an appropriate value of .

Use a calculator to evaluate the expression. Round your answer to six decimal places.

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

Use properties of logarithms or a definition to simplify the expression. If find .

Use properties of logarithms or a definition to simplify the expression. If , find .

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 6: Exponential and Logarithmic Functions

Graph the function. ​ ​

Write the expression as the sum or difference of two logarithmic functions containing no exponents.

Use a calculator to determine whether expression (a) is equivalent to expression (b). ​ ​

Graph the function . ​

Use the formula to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $900 at interest rate 9% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places. ​

Solve for x by writing the equation in exponential form. ​ ​

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

The monthly sales S for a product is given by , where x is the number of months that have passed since the end of a promotional campaign. How many months after the end of the campaign will sales drop below 6,000, if no new campaign is initiated? Round to two decimal places. ​

Use a calculator to evaluate the expression. Round your answer to two decimal places, if necessary. ​

If $4,000 is invested at an annual rate of 8% compounded continuously, the future value S at any time t (in years) is given by . How long does it take for the investment to double? Round your answer to one decimal place. ​

Find an equivalent expression for the given logarithm using the change-of-base formula. ​ ​

Graph the function. ​ ​

Express in the form with an appropriate value of . ​

Use a calculator to evaluate the expression. Round your answer to six decimal places. ​ ​

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

Use properties of logarithms or a definition to simplify the expression. ​ If find . ​

Use properties of logarithms or a definition to simplify the expression. ​ If , find . ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Graph the function.

Use a calculator to determine whether expression (a) is equivalent to expression (b).

Graph the function .

Use the formula to find the doubling time t, in years, for an investment at r% compounded n times per year. Suppose you make an investment of $900 at interest rate 9% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places.

Solve for x by writing the equation in exponential form.

The monthly sales S for a product is given by , where x is the number of months that have passed since the end of a promotional campaign. How many months after the end of the campaign will sales drop below 6,000, if no new campaign is initiated? Round to two decimal places.

Use a calculator to evaluate the expression. Round your answer to two decimal places, if necessary.

If $4,000 is invested at an annual rate of 8% compounded continuously, the future value S at any time t (in years) is given by . How long does it take for the investment to double? Round your answer to one decimal place.

Find an equivalent expression for the given logarithm using the change-of-base formula.

Graph the function.

Express in the form with an appropriate value of .

Use a calculator to evaluate the expression. Round your answer to six decimal places.

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

Use properties of logarithms or a definition to simplify the expression. If find .

Use properties of logarithms or a definition to simplify the expression. If , find .