Question 1

Solve the logarithmic equation   . Round your answer to three decimal places. ​

Accepted Answer

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

Question 2

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation ​   .
​
Graph this equation for 0 ≤ t ≤ 30.
​

Accepted Answer

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

Question 3

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 4

Write the equation in exponential form. ​   ​

Accepted Answer

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

Question 5

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 6

Which answer choice is a graph of the function? ​   ​

Accepted Answer

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

Question 7

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula   applies to the growth of the country's population. Estimate the population of the country in 2010. Round your answer to the nearest human. ​

Accepted Answer

A)  ​149,182 
B)  ​332,012 
C)  ​222,554 
D)  ​67,032 
E)  ​44,933 
A)  ​149,182 
B)  ​332,012 
C)  ​222,554 
D)  ​67,032 
E)  ​44,933

Question 8

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 9

Write the equation in logarithmic form. ​   ​

Accepted Answer

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

Question 10

If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by   . How long does it take for the investment to double? Round your answer to one decimal place. ​

Accepted Answer

A)  91.2 months 
B)  14.8 months 
C)  76.0 months 
D)  92.2 months 
E)  68.7 months 
A)  91.2 months 
B)  14.8 months 
C)  76.0 months 
D)  92.2 months 
E)  68.7 months

Question 11

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 12

The consumer price index (CPI) is calculated by averaging the prices of various items after assigning a weight to each item. The following table gives the consumer price indexes for selected years from 1940 through 2002, reflecting buying patterns of all urban consumers. Find an equation that models these data and use it to determine when the consumer price index will pass 349. ​
 
Source: U.S. Bureau of the Census
​

Accepted Answer

A)  The 2011 - 2012 year 
B)  The 2012 - 2013 year 
C)  The 2014 - 2015 year 
D)  The 2016 - 2017 year 
E)  The 2019 - 2020 year 
A)  The 2011 - 2012 year 
B)  The 2012 - 2013 year 
C)  The 2014 - 2015 year 
D)  The 2016 - 2017 year 
E)  The 2019 - 2020 year

Question 13

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 14

The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by   , where t represents time in months since she assumed office. What will be the sales after 9 months? Round your answer to the nearest month. ​

Accepted Answer

A)  ​2,931 
B)  ​1 
C)  ​6 
D)  ​1,620 
E)  ​75 
A)  ​2,931 
B)  ​1 
C)  ​6 
D)  ​1,620 
E)  ​75

Question 15

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). How many are infected after 7 days? ​

Accepted Answer

A)  approximately 32 students 
B)  approximately 10 students 
C)  approximately 9,905 students 
D)  approximately 928 students 
E)  approximately 911 students 
A)  approximately 32 students 
B)  approximately 10 students 
C)  approximately 9,905 students 
D)  approximately 928 students 
E)  approximately 911 students

Question 16

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 $1,300 at interest rate 11% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places. ​

Accepted Answer

A)  2.13 years 
B)  12.78 years 
C)  3.19 years 
D)  3.32 years 
E)  6.39 years 
A)  2.13 years 
B)  12.78 years 
C)  3.19 years 
D)  3.32 years 
E)  6.39 years

Question 17

Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to   , where   is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times   . ​

Accepted Answer

A)  3 
B)  30 
C)  4 
D)  300 
E)  100 
A)  3 
B)  30 
C)  4 
D)  300 
E)  100

Question 18

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

Accepted Answer

A)  0.0002 
B)  3.4641 
C)  0.2887 
D)  8,192 
E)  6 
A)  0.0002 
B)  3.4641 
C)  0.2887 
D)  8,192 
E)  6

Question 19

If $1,200 is invested for x years at an annual rate of 7%, compounded quarterly, the future value that will result is ​   ​
Determine the value of the investment after 8 years. Round your answer to two decimal places, if necessary.
​

Accepted Answer

A)  $5,229.16 
B)  $10,458.32 
C)  $2,061.82 
D)  $9,258.32 
E)  $672 
A)  $5,229.16 
B)  $10,458.32 
C)  $2,061.82 
D)  $9,258.32 
E)  $672

Question 20

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with   ) is given by the equation   . What is the concentration after 6 hours? Round your answer to one decimal place. ​

Accepted Answer

A)  106.3 
B)  ​1,499.1 
C)  222.0 
D)  40,242.9 
E)  93.7 
A)  106.3 
B)  ​1,499.1 
C)  222.0 
D)  40,242.9 
E)  93.7

Solve the logarithmic equation . Round your answer to three decimal places.

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation . Graph this equation for 0 ≤ t ≤ 30.

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

Write the equation in exponential form.

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

Which answer choice is a graph of the function?

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2010. Round your answer to the nearest human.

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

Write the equation in logarithmic form.

If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by . How long does it take for the investment to double? Round your answer to one decimal place.

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

The president of a company predicts that sales N will increase after she assumes office and that the number of monthly sales will follow the curve given by , where t represents time in months since she assumed office. What will be the sales after 9 months? Round your answer to the nearest month.

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). How many are infected after 7 days?

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 $1,300 at interest rate 11% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places.

Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to , where is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times .

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

If $1,200 is invested for x years at an annual rate of 7%, compounded quarterly, the future value that will result is Determine the value of the investment after 8 years. Round your answer to two decimal places, if necessary.

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation . What is the concentration after 6 hours? Round your answer to one decimal place.

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 5: Exponential and Logarithmic Functions

Solve the logarithmic equation . Round your answer to three decimal places. ​

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation ​ . ​ Graph this equation for 0 ≤ t ≤ 30. ​

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

Write the equation in exponential form. ​ ​

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

Which answer choice is a graph of the function? ​ ​

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2010. Round your answer to the nearest human. ​

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

Write the equation in logarithmic form. ​ ​

If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by . How long does it take for the investment to double? Round your answer to one decimal place. ​

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

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). How many are infected after 7 days? ​

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 $1,300 at interest rate 11% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places. ​

Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to , where is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times . ​

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

If $1,200 is invested for x years at an annual rate of 7%, compounded quarterly, the future value that will result is ​ ​ Determine the value of the investment after 8 years. Round your answer to two decimal places, if necessary. ​

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation . What is the concentration after 6 hours? Round your answer to one decimal place. ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Solve the logarithmic equation . Round your answer to three decimal places.

The percent concentration y of a certain drug in the bloodstream at any time t in minutes is given by the equation . Graph this equation for 0 ≤ t ≤ 30.

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

Write the equation in exponential form.

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

Which answer choice is a graph of the function?

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2010. Round your answer to the nearest human.

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

Write the equation in logarithmic form.

If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by . How long does it take for the investment to double? Round your answer to one decimal place.

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

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). How many are infected after 7 days?

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 $1,300 at interest rate 11% compounded quarterly. How long will it take for your investment to double? Round your answer to two decimal places.

Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to , where is the threshold of hearing for the average human ear. Find the loudness when I is 1,000 times .

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

If $1,200 is invested for x years at an annual rate of 7%, compounded quarterly, the future value that will result is Determine the value of the investment after 8 years. Round your answer to two decimal places, if necessary.

The concentration y of a certain drug in the bloodstream t hours after an oral dosage (with ) is given by the equation . What is the concentration after 6 hours? Round your answer to one decimal place.