Question 1

Identify the operation that will transform the graph of   into the graph of   .

Accepted Answer

A) g(x) is obtained by reflecting f(x) in the x-axis then shifting upward 2 units. 
B) g(x) is obtained by reflecting f(x) in the y-axis then shifting upward 2 units. 
C) g(x) is obtained by reflecting f(x) in the x-axis then shifting downward 2 units. 
D) g(x) is obtained by reflecting f(x) in the y-axis then shifting downward 2 units. 
E) g(x) cannot be obtained by any of these tranforms. 
A) g(x) is obtained by reflecting f(x) in the x-axis then shifting upward 2 units. 
B) g(x) is obtained by reflecting f(x) in the y-axis then shifting upward 2 units. 
C) g(x) is obtained by reflecting f(x) in the x-axis then shifting downward 2 units. 
D) g(x) is obtained by reflecting f(x) in the y-axis then shifting downward 2 units. 
E) g(x) cannot be obtained by any of these tranforms.

Question 2

Write the exponential equation   in logarithmic form.

Accepted Answer

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

Question 3

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.

Question 4

Sketch the graph of the function   .

Accepted Answer

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

Question 5

The chemical acidity of a solution is measured in units of pH:   , where [H+] is the hydrogen ion concentration in the solution. What is the pH if   ? Round to the nearest hundredth.

Accepted Answer

A) 4.15 
B) 3.85 
C) 7.26 
D) 3.15 
E)    
A) 4.15 
B) 3.85 
C) 7.26 
D) 3.15 
E)

Question 6

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

Accepted Answer

A) -1.680 
B) 1.816 
C) -1.816 
D) 0.229 
E) undefined 
A) -1.680 
B) 1.816 
C) -1.816 
D) 0.229 
E) undefined

Question 7

An initial investment of $5000 doubles in value in 11 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Accepted Answer

A) 2.7% 
B) 3.2% 
C) 11% 
D) 6.3% 
E) 100% 
A) 2.7% 
B) 3.2% 
C) 11% 
D) 6.3% 
E) 100%

Question 8

Rewrite the logarithmic equation   in exponential form.

Accepted Answer

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

Question 9

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 100 years. Round to the nearest hundredth of a gram.

Accepted Answer

A) 0.00 g 
B) 0.16 g 
C) 0.96 g 
D) 4.79 g 
E) 5.00 g 
A) 0.00 g 
B) 0.16 g 
C) 0.96 g 
D) 4.79 g 
E) 5.00 g

Question 10

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 11

Condense the expression   to the logarithm of a single term.

Accepted Answer

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

Question 12

Find the exact value of   without using a calculator.

Accepted Answer

A) 2.25 
B) 9 
C) 4 
D) 5 
E) 4.5 
A) 2.25 
B) 9 
C) 4 
D) 5 
E) 4.5

Question 13

The population P of a culture of bacteria is described by the equation   , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at t = 3 hours? After how many hours will the population reach 7000? Round to the nearest tenth of an hour.

Accepted Answer

A) approximate population   when   after 164 hours,   
B) approximate population   when   after 1.6 hours,   
C) approximate population   when   after   hours,   
D) approximate population   when   after 7.2 hours,   
E) approximate population   when   after 8.9 hours,   
A) approximate population   when   after 164 hours,   
B) approximate population   when   after 1.6 hours,   
C) approximate population   when   after   hours,   
D) approximate population   when   after 7.2 hours,   
E) approximate population   when   after 8.9 hours,

Question 14

Approximate the solution of   to 3 decimal places. (You may use a graphing utility.)

Accepted Answer

A) -3.253 
B) 0.539 
C) -0.639 
D) 2.989 
E) 0.187 
A) -3.253 
B) 0.539 
C) -0.639 
D) 2.989 
E) 0.187

Question 15

Simplify the expression   .

Accepted Answer

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

Question 16

Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is 14C is constant. The amount of 14C in an object made from harvested plants, like paper, will decline exponentially according to the equation   , where A represents the amount of 14C in the object, Ao represents the amount of 14C in living organisms, and t is the time in years since the plant was harvested. If an archeological artifact has 25% as much 14C as a living organism, how old would you predict it to be? Round to the nearest year.

Accepted Answer

A) 26,536 years 
B) 5715 years 
C) 11,429 years 
D) 13,967 years 
E) 107 years 
A) 26,536 years 
B) 5715 years 
C) 11,429 years 
D) 13,967 years 
E) 107 years

Question 17

The population P of a bacteria culture is modeled by   , where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Accepted Answer

A) 51.0 hours 
B) 49.2 hours 
C) 63.5 hours 
D) 61.7 hours 
E) 7.9 hours 
A) 51.0 hours 
B) 49.2 hours 
C) 63.5 hours 
D) 61.7 hours 
E) 7.9 hours

Question 18

Identify the operation that will transform the graph of   into the graph of   .

Accepted Answer

A) g(x) is obtained by shifting f(x) 2 units upward (positive). 
B) g(x) is obtained by shifting f(x) 2 units downward (negative). 
C) g(x) is obtained by shifting f(x) 2 units to the left (negative). 
D) g(x) is obtained by shifting f(x) 2 units to the right (positive). 
E) g(x) cannot be obtained by any of these tranforms. 
A) g(x) is obtained by shifting f(x) 2 units upward (positive). 
B) g(x) is obtained by shifting f(x) 2 units downward (negative). 
C) g(x) is obtained by shifting f(x) 2 units to the left (negative). 
D) g(x) is obtained by shifting f(x) 2 units to the right (positive). 
E) g(x) cannot be obtained by any of these tranforms.

Question 19

Approximate the solution to   . Round to 3 decimal places.

Accepted Answer

A) 2.906 
B) 8.178 
C) 4.299 
D) 0.065 
E) 528.298 
A) 2.906 
B) 8.178 
C) 4.299 
D) 0.065 
E) 528.298

Question 20

Solve   for x.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Identify the operation that will transform the graph of into the graph of .

Write the exponential equation in logarithmic form.

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

Sketch the graph of the function ^.

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution. What is the pH if ? Round to the nearest hundredth.

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

An initial investment of $5000 doubles in value in 11 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Rewrite the logarithmic equation in exponential form.

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 100 years. Round to the nearest hundredth of a gram.

Condense the expression to the logarithm of a single term.

Condense the expression to the logarithm of a single term.

Find the exact value of without using a calculator.

The population P of a culture of bacteria is described by the equation , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at t = 3 hours? After how many hours will the population reach 7000? Round to the nearest tenth of an hour.

Approximate the solution of to 3 decimal places. (You may use a graphing utility.)

Simplify the expression .

The population P of a bacteria culture is modeled by , where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Identify the operation that will transform the graph of into the graph of .

Approximate the solution to . Round to 3 decimal places.

Solve for x.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 8: Exponential and Logarithmic Functions

Identify the operation that will transform the graph of into the graph of .

Write the exponential equation in logarithmic form.

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

Sketch the graph of the function .

The chemical acidity of a solution is measured in units of pH: , where [H+] is the hydrogen ion concentration in the solution. What is the pH if ? Round to the nearest hundredth.

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

An initial investment of $5000 doubles in value in 11 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

Rewrite the logarithmic equation in exponential form.

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 100 years. Round to the nearest hundredth of a gram.

Condense the expression to the logarithm of a single term.

Condense the expression to the logarithm of a single term.

Find the exact value of without using a calculator.

The population P of a culture of bacteria is described by the equation , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at t = 3 hours? After how many hours will the population reach 7000? Round to the nearest tenth of an hour.

Approximate the solution of to 3 decimal places. (You may use a graphing utility.)

Simplify the expression .

The population P of a bacteria culture is modeled by , where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

Identify the operation that will transform the graph of into the graph of .

Approximate the solution to . Round to 3 decimal places.

Solve for x.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Sketch the graph of the function ^.

The chemical acidity of a solution is measured in units of pH: , where [H⁺] is the hydrogen ion concentration in the solution. What is the pH if ? Round to the nearest hundredth.

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 100 years. Round to the nearest hundredth of a gram.