Question 1

Rewrite the exponential equation   in logarithmic form.

Accepted Answer

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

Question 2

Solve the equation   for x using the One-to-One Property.

Accepted Answer

A) 11 
B) -9 
C) -11 
D) 0 
E) The equation has no solution. 
A) 11 
B) -9 
C) -11 
D) 0 
E) The equation has no solution. B

Question 3

Evaluate the function   at   . Round to 3 decimal places.

Accepted Answer

A) 2.700 
B) 2.075 
C) 2.250 
D) 5.203 
E) 2.415 
A) 2.700 
B) 2.075 
C) 2.250 
D) 5.203 
E) 2.415 B

Question 4

Use a graphing utility to determine which graph below is the graph of the function.

Accepted Answer

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

Question 5

Graph the exponential function.

Accepted Answer

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

Question 6

What is the value of the function   at   ? Round to 3 decimal places.

Accepted Answer

A) 42.051 
B) 37.296 
C) 7.597 
D) 26.492 
E) 82.783 
A) 42.051 
B) 37.296 
C) 7.597 
D) 26.492 
E) 82.783

Question 7

Let Q represent a mass of radioactive radium (226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is   Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.

Accepted Answer

A) 0.00 g 
B) 0.47 g 
C) 0.88 g 
D) 4.39 g 
E) 5.00 g 
A) 0.00 g 
B) 0.47 g 
C) 0.88 g 
D) 4.39 g 
E) 5.00 g

Question 8

Find the value of x.

Accepted Answer

A) x = 81 
B) x = 3 
C) x = 4 
D) x = 41 
A) x = 81 
B) x = 3 
C) x = 4 
D) x = 41

Question 9

Graph the function using translations.

Accepted Answer

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

Question 10

Simplify the expression   .

Accepted Answer

A)    
B)    
C) 6 
D)    
E) The expression cannot be simplified. 
A)    
B)    
C) 6 
D)    
E) The expression cannot be simplified.

Question 11

Let Q represent a mass of radioactive radium (226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is   Determine the quantity present after 200 years. Round to the nearest hundredth of a gram.

Accepted Answer

A) 3.67 g 
B) 4.00 g 
C) 0.25 g 
D) 0.92 g 
E) 0.00 g 
A) 3.67 g 
B) 4.00 g 
C) 0.25 g 
D) 0.92 g 
E) 0.00 g

Question 12

Use a calculator to find the value for   to four decimal places.

Accepted Answer

A) -0.1497 
B) -0.3449 
C) 0.8502 
D) -0.8502 
E) 0.1497 
A) -0.1497 
B) -0.3449 
C) 0.8502 
D) -0.8502 
E) 0.1497

Question 13

Rewrite the logarithm   in terms of the natural logarithm.

Accepted Answer

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

Question 14

Simplify the expression   .

Accepted Answer

A) The expression cannot be simplified. 
B) 3 
C) -6 
D) 1 
E) -27 
A) The expression cannot be simplified. 
B) 3 
C) -6 
D) 1 
E) -27

Question 15

Solve for x:   . Round to 3 decimal places.

Accepted Answer

A) 2.407 
B) 0.407 
C) 1.362 
D) -1.362 
E) no solution 
A) 2.407 
B) 0.407 
C) 1.362 
D) -1.362 
E) no solution

Question 16

Write the exponential equation   in logarithmic form.

Accepted Answer

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

Question 17

Evaluate the function   at   . Round to 3 decimal places. (You may use your calculator.)

Accepted Answer

A) 2.079 
B) -13.038 
C) 13.038 
D) -6.125 
E) undefined 
A) 2.079 
B) -13.038 
C) 13.038 
D) -6.125 
E) undefined

Question 18

The chemical acidity of a solution is measured in units of pH:   , where   is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.4, how many times higher is its   than pure water's, which has a pH of 7?

Accepted Answer

A)    
B)    
C) 7 
D)    
E)    
A)    
B)    
C) 7 
D)    
E)

Question 19

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 60 grams, how much will remain after 81 years?

Accepted Answer

A) 2.8307 grams 
B) 0.6483 grams 
C) 15.0000 grams 
D) 53.9595 grams 
E) 0.0000 grams 
A) 2.8307 grams 
B) 0.6483 grams 
C) 15.0000 grams 
D) 53.9595 grams 
E) 0.0000 grams

Question 20

Evaluate the function   at   . Round to 3 decimal places.

Accepted Answer

A) 5.287 
B) 4.680 
C) 20.055 
D) 2.572 
E) 1.690 
A) 5.287 
B) 4.680 
C) 20.055 
D) 2.572 
E) 1.690

Rewrite the exponential equation in logarithmic form.

Solve the equation for x using the One-to-One Property.

Evaluate the function at . Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function.

Graph the exponential function.

What is the value of the function at ? Round to 3 decimal places.

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.

Find the value of x.

Graph the function using translations.

Simplify the expression .

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 200 years. Round to the nearest hundredth of a gram.

Use a calculator to find the value for to four decimal places.

Rewrite the logarithm in terms of the natural logarithm.

Simplify the expression .

Solve for x: . Round to 3 decimal places.

Write the exponential equation in logarithmic form.

Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.4, how many times higher is its than pure water's, which has a pH of 7?

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 60 grams, how much will remain after 81 years?

Evaluate the function at . Round to 3 decimal places.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters

Exam 4: Exponential and Logarithmic Functions

Rewrite the exponential equation in logarithmic form.

Solve the equation for x using the One-to-One Property.

Evaluate the function at . Round to 3 decimal places.

Use a graphing utility to determine which graph below is the graph of the function.

Graph the exponential function.

What is the value of the function at ? Round to 3 decimal places.

Let Q represent a mass of radioactive radium (226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.

Find the value of x.

Graph the function using translations.

Simplify the expression .

Let Q represent a mass of radioactive radium (226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 200 years. Round to the nearest hundredth of a gram.

Use a calculator to find the value for to four decimal places.

Rewrite the logarithm in terms of the natural logarithm.

Simplify the expression .

Solve for x: . Round to 3 decimal places.

Write the exponential equation in logarithmic form.

Evaluate the function at . Round to 3 decimal places. (You may use your calculator.)

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.4, how many times higher is its than pure water's, which has a pH of 7?

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 60 grams, how much will remain after 81 years?

Evaluate the function at . Round to 3 decimal places.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 300 years. Round to the nearest hundredth of a gram.

Let Q represent a mass of radioactive radium (²²⁶Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 200 years. Round to the nearest hundredth of a gram.