Deck 8: Exponential and Logarithmic Functions

Question 1

Evaluate the function at x = 3.6. Round to 3 decimal places.

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

Answer 1

2.572

Question 2

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

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

Answer 2

-1.816

Question 3

Sketch the graph of the function ^.

A)
B)
C)
D)
E)

Answer 3

Question 4

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

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 5

Identify the x-intercept of the function .

A)x = 1
B)x = 0
C)x = 4
D)x = 2
E)The function has no x-intercept.

Question 6

Evaluate the function without using a calculator.

A)0
B)-1
C)-2
D)4
E)

Question 7

Sketch the graph of the function ^.

A)
B)
C)
D)
E)

Question 8

What is the value of the function at x = 2.3? Round to 3 decimal places.

A)118.806
B)91.605
C)1.851
D)76.221
E)216.302

Question 9

What is the value of the function at x = 2.5? Round to 3 decimal places.

A)0.603
B)0.047
C)7.344
D)-38.124
E)0.000

Question 10

Evaluate the function without using a calculator.

A)-2
B)
C)2
D)
E)undefined

Question 11

Evaluate the function at x = 240. Round to 3 decimal places.

A)3.310
B)96,480.000
C)1324.082
D)1764.558
E)404.010

Question 12

Use a graphing utility to graph the function.

A)
B)
C)
D)
E)

Question 13

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

A)1.546
B)0.671
C)1.280
D)-0.347
E)undefined

Question 14

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 15

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.

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

Question 16

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

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 17

Write the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 18

Identify the x-intercept of the function .

A)
B)
C)-4
D)8
E)The function has no x-intercept.

Question 19

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 20

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 21

Approximate the solution to . Round to 3 decimal places.

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

Question 22

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

A)
B)
C)
D)
E)

Question 23

Find the exact value of without using a calculator.

A)
B)1
C)11
D)
E)4

Question 24

An initial investment of $7000 grows at an annual interest rate of 3% compounded continuously. How long will it take to double the investment?

A)23.10 years
B)24.10 years
C)24.00 years
D)23.00 years
E)1 year

Question 25

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

A)8.792
B)12.294
C)7.222
D)-6.489
E)7.511

Question 26

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

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

Question 27

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

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

Question 28

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 29

Approximate the solution to . Round to 3 decimal places.

A)-0.632
B)0.333
C)1.164
D)2.718
E)0.222

Question 30

Simplify the expression .

A)4
B)-8
C)2
D)-36
E)The expression cannot be simplified.

Question 31

Find the exact value of without using a calculator.

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

Question 32

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 33

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 34

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

A)0.395
B)-0.434
C)-2.778
D)-0.360
E)0.172

Question 35

Identify the graph that represents the function.

A)
B)
C)
D)
E)

Question 36

Solve for x.

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

Question 37

Use a graphing utility to approximate the solution to . Round to 3 decimal places.

A)4.772
B)3.772
C)2.386
D)1.886
E)no solution

Question 38

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

A)6.303
B)0.309
C)3.239
D)12.264
E)2.737

Question 39

Solve for x.

A)1
B)
C)
D)
E)no solution

Question 40

Simplify the expression .

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

Question 41

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.

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 42

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

A)1.58
B)6.31
C)6.31
D)1.58
E)3.800

Question 43

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

Question 44

An investment is expected to pay 5% per year compounded continuously. If you want the value of the investment to be $900,000 after 25 years, how much should you invest initially? Round to the nearest dollar.

A)$64,464
B)$128,927
C)$257,854
D)$515,709
E)$429,203

Question 45

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.

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

Question 46

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 25% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year.

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

Question 47

The value of an investment is presently $9186.79. It had been paying 8% compounded continuously since the investment was made 10 years ago. How much was invested originally?

A)$3699.15
B)$4127.89
C)$5076.14
D)$5973.34
E)$1456.01

Question 48

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.

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