Deck 6: Exponential and Logarithmic Functions

Question 1

Identify the value of the function at . Round to 3 decimal places.

A) 6.028
B) 3.618
C) 2.618
D) 4.118
E) 3.118

Answer 1

2.618

Question 2

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Answer 2

Question 3

Sketch the graph of the function

Answer 3

Question 4

Use the One-to-One Property to solve the following equation for x.

A)
B)
C)
D) 2
E)

Question 5

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

A) -3.391
B) 3.391
C) undefined
D) -2.928
E) 2.150

Question 6

Identify the x-intercept of the function .

A)
B) The function has no x-intercept.
C)
D)
E)

Question 7

Evaluate the function at without using a calculator.

A)
B) -4
C) -2
D) 27
E) -3

Question 8

Write the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 9

Identify the graph of the function.

A)
B)
C)
D)
E)

Question 10

Evaluate the function at . Round to 3 decimal places.

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

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

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

Question 12

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

A) 1.398
B) 0.676
C) -7.747
D) 0.848
E) 1.795

Question 13

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 14

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

A) undefined
B) 0.876
C) 0.147
D) 0.339
E) -0.347

Question 15

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

A)
B)
C)
D)
E)

Question 16

Use the One-to-One Property to solve the following equation for x.

A)
B)
C)
D)
E)

Question 17

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

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

Question 18

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

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

Question 19

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 20

Evaluate the function at . Round to 3 decimal places.

A) 736.228
B) 803.695
C) 303.008
D) 54,270.000
E) 2.454

Question 21

Solve for x: . Round to 3 decimal places.

A) 7.587
B) 13.291
C) -3.794
D) -13.291
E) 10.518

Question 22

Find the exact value of without using a calculator.

A) 1
B) 4
C) 9
D)
E)

Question 23

Find the exact value of without using a calculator.

A) 5
B) 2.5
C) 1.25
D) 2
E) 3

Question 24

An initial investment of $3000 doubles in value in 8.3 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

A) 8.4%
B) 3.6%
C) 4.2%
D) 8.3%
E) 100%

Question 25

Simplify the expression .

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

Question 26

Rewrite the logarithm in terms of the common logarithm (base 10).

A)
B)
C)
D)
E)

Question 27

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.

A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623

Question 28

Which investment option will pay the most interest?

A) 11.2% compounded quarterly
B) 11.4% compounded semiannually
C) 11.0% compounded continuously
D) These investments all pay the same amount of interest.
E) 11.6% compounded annually

Question 29

Determine whether or not is a solution to .

A) no
B) yes

Question 30

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 31

The pH of an acidic solution is a measure of the concentration of the acid particles in the solution, with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the solution. In this experiment, the pH changes according to the equation , where x is the number of grams of antacid added to the solution. What is the pH of the solution after the addition of 0.1 grams of antacid tablet?

A) 5.14
B) 4.44
C) -0.18
D) 4.78
E) 4.96

Question 32

Simplify the expression .

A) 4
B) The expression cannot be simplified.
C) -12
D) -108
E) 1

Question 33

Evaluate the logarithm using the change of base formula. Round to 3 decimal places.

A) -1.745
B) -0.692
C) 0.630
D) 0.273
E) -0.573

Question 34

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 35

Solve for x.

A) -5
B) -1
C) -3
D) 1
E) no solution

Question 36

Put the expressions in the appropriate order: .

A)
B)
C) The expressions are equivalent.
D)
E)

Question 37

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 38

Find the exact value of without using a calculator.

A)
B)
C)
D) -1
E)

Question 39

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Question 40

Solve for x: . Round to 3 decimal places.

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

Question 41

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution. What is if the ?

A) 8.800
B)
C)
D)
E)

Question 42

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 1600.
(a) What was the population at hours? Show your work.
(b) After how many hours will the population reach 8000? Round to the nearest tenth of an hour. Show your work.

Question 43

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, A_o 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 40% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year.

A) 5715 years
B) 30,411 years
C) 87 years
D) 7554 years
E) 16,006 years

Question 44

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 3.2, how many times higher is its than pure water's, which has a pH of 7?

A)
B)
C) 7
D)
E)

Question 45

An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?

A) 1 year
B) 14.40 years
C) 13.86 years
D) 14.86 years
E) 13.40 years

Question 46

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.

A) 57.5 hours
B) 9.6 hours
C) 92.7 hours
D) 94.5 hours
E) 59.3 hours