Question 1

If   is in the domain of   , find

Accepted Answer

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

Question 2

An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by   where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .

Accepted Answer

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

Question 3

The function   gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.

Accepted Answer

A) 231 mg 
B) 182 mg 
C) 249 mg 
D) 4 mg 
E) 15 mg 
A) 231 mg 
B) 182 mg 
C) 249 mg 
D) 4 mg 
E) 15 mg

Question 4

Write   as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Accepted Answer

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

Question 5

Use composition of functions to determine whether   and   are inverses of one another.

Accepted Answer

A) True 
 B)False

Question 6

Estimate the percentage of radioactive material that remains in a sample after 3 years if the half-life of the material is 261 days. Round to the nearest hundredth of a percent.

Accepted Answer

A) 0.42% 
B) 5.46% 
C) 0.97% 
D) 11.92% 
E) 28.28% 
A) 0.42% 
B) 5.46% 
C) 0.97% 
D) 11.92% 
E) 28.28%

Question 7

An earthquake in South America had an intensity of   . What did it measure on the Richter scale?

Accepted Answer

A) 1.3 
B) 7.7 
C) 2.0 
D) 17.7 
E) 5.0 
A) 1.3 
B) 7.7 
C) 2.0 
D) 17.7 
E) 5.0

Question 8

A cup of coffee is heated to   F and placed in a room that maintains a temperature of   F. The temperature of the coffee after t minutes is given by   . Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach   F.

Accepted Answer

A) 26.8 min 
B) 2.9 min 
C)    min 
D) 13.6 min 
E) 42.3 min 
A) 26.8 min 
B) 2.9 min 
C)    min 
D) 13.6 min 
E) 42.3 min

Question 9

Use algebraic procedures to find the exact solution of the equation   .

Accepted Answer

A) 3 
B) 1 
C) 243 
D) 7 
E) 729 
A) 3 
B) 1 
C) 243 
D) 7 
E) 729

Question 10

Write the expression below as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Accepted Answer

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

Question 11

Find the domain of the function   .

Accepted Answer

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

Question 12

The monthly earnings in dollars, of a software sales executive is given by   where s is the value, in dollars, of the software sold by the executive during the month. Find

Accepted Answer

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

Question 13

A cup of coffee is heated to 160 F and placed in a room that maintains a temperature of 60 F. The temperature of the coffee after t minutes is given by   . Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.

Accepted Answer

A) 82° F 
B) 123° F 
C) 115° F 
D) 35° F 
E) 56° F 
A) 82° F 
B) 123° F 
C) 115° F 
D) 35° F 
E) 56° F

Question 14

Evaluate the logarithm below.

Accepted Answer

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

Question 15

Find the decay function for the amount of radioactive material that remains in a sample after t days if the half-life of the material is 29 days.

Accepted Answer

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

Question 16

If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by   . Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.

Accepted Answer

A) 0.07 ft/sec 
B) 13.75 ft/sec 
C) 0.16 ft/sec 
D) 16.93 ft/sec 
E) 14.84 ft/sec 
A) 0.07 ft/sec 
B) 13.75 ft/sec 
C) 0.16 ft/sec 
D) 16.93 ft/sec 
E) 14.84 ft/sec

Question 17

Find   .

Accepted Answer

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

Question 18

If f is a one-to-one function and

Accepted Answer

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

Question 19

Use a scatter plot to determine the type of function that will provide the best model for the data   .

Accepted Answer

A) an increasing exponential function 
B) an increasing linear function 
C) a decreasing exponential function 
D) a decreasing logarithmic function 
E) an increasing logarithmic function 
A) an increasing exponential function 
B) an increasing linear function 
C) a decreasing exponential function 
D) a decreasing logarithmic function 
E) an increasing logarithmic function

Question 20

The demand d for a specific product, in items per month, is given by   where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?

Accepted Answer

A) The demand will approach 0 items per month. 
B) The demand will approach   items per month. 
C) The demand will approach   items per month. 
D) The demand will approach   items per month. 
E) The demand will increase without bound. 
A) The demand will approach 0 items per month. 
B) The demand will approach   items per month. 
C) The demand will approach   items per month. 
D) The demand will approach   items per month. 
E) The demand will increase without bound.

If is in the domain of , find

An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .

The function gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.

Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Use composition of functions to determine whether and are inverses of one another.

Estimate the percentage of radioactive material that remains in a sample after 3 years if the half-life of the material is 261 days. Round to the nearest hundredth of a percent.

An earthquake in South America had an intensity of . What did it measure on the Richter scale?

A cup of coffee is heated to F and placed in a room that maintains a temperature of F. The temperature of the coffee after t minutes is given by . Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach F.

Use algebraic procedures to find the exact solution of the equation .

Write the expression below as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Find the domain of the function .

The monthly earnings in dollars, of a software sales executive is given by where s is the value, in dollars, of the software sold by the executive during the month. Find

A cup of coffee is heated to 160 F and placed in a room that maintains a temperature of 60 F. The temperature of the coffee after t minutes is given by . Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.

Evaluate the logarithm below.

Find the decay function for the amount of radioactive material that remains in a sample after t days if the half-life of the material is 29 days.

If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by . Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.

Find .

If f is a one-to-one function and

Use a scatter plot to determine the type of function that will provide the best model for the data .

The demand d for a specific product, in items per month, is given by where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

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Exam 4: Exponential and Logarithmic Functions

If is in the domain of , find

An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .

The function gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.

Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Use composition of functions to determine whether and are inverses of one another.

Estimate the percentage of radioactive material that remains in a sample after 3 years if the half-life of the material is 261 days. Round to the nearest hundredth of a percent.

An earthquake in South America had an intensity of . What did it measure on the Richter scale?

A cup of coffee is heated to F and placed in a room that maintains a temperature of F. The temperature of the coffee after t minutes is given by . Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach F.

Use algebraic procedures to find the exact solution of the equation .

Write the expression below as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.

Find the domain of the function .

The monthly earnings in dollars, of a software sales executive is given by where s is the value, in dollars, of the software sold by the executive during the month. Find

A cup of coffee is heated to 160 F and placed in a room that maintains a temperature of 60 F. The temperature of the coffee after t minutes is given by . Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.

Evaluate the logarithm below.

Find the decay function for the amount of radioactive material that remains in a sample after t days if the half-life of the material is 29 days.

If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by . Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.

Find .

If f is a one-to-one function and

Use a scatter plot to determine the type of function that will provide the best model for the data .

The demand d for a specific product, in items per month, is given by where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters