Deck 4: Exponential and Logarithmic Functions

Question 1

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

A) -2.241
B) undefined
C) 1.707
D) 4.272
E) -1.707

Answer 1

-1.707

Question 2

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.

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

Answer 2

3.67 g

Question 3

Find the exact value of without using a calculator.

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

Answer 3

Question 4

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 5

Simplify the expression .

A) The expression cannot be simplified.
B) 2
C) 3
D) -3
E) -9

Question 6

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 7

Evaluate the function at . Round to 3 decimal places.

A) 4.190
B) 4.590
C) 14.611
D) 5.412
E) 2.890

Question 8

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

A)
B)
C)
D)
E)

Question 9

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Question 10

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

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

Question 11

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

A) 2.061
B) 4.745
C) 3.061
D) 3.561
E) 2.561

Question 12

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

A) -12.354
B) 0.089
C) 0.039
D) -0.098
E) -0.081

Question 13

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 14

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

A) 26.822
B) 99.373
C) 45.553
D) 599.708
E) 7.721

Question 15

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 16

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

A) 2.468
B) 2.921
C) 11.060
D) 5.684
E) 0.342

Question 17

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 18

Identify the x-intercept of the function .

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

Question 19

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 20

Simplify the expression .

A) 9
B)
C)
D) The expression cannot be simplified.
E)

Question 21

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

A) 6.572
B) 3.354
C) 2.854
D) 3.854
E) 4.354

Question 22

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 23

An initial investment of $1000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?

A) 10.29 years
B) 9.29 years
C) 9.90 years
D) 10.90 years
E) 1 year

Question 24

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

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

Question 25

Find the exact value of without using a calculator.

A) 3
B) 2
C) 1.5
D) 0.75
E) 1

Question 26

Simplify the expression .

A)
B)
C) 3
D)
E) The expression cannot be simplified.

Question 27

Identify the x-intercept of the function .

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

Question 28

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

A)
B)
C)
D)
E) 2

Question 29

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

A) -1
B) -101
C) -99
D) The equation has no solution.
E) 101

Question 30

Evaluate the function at . Round to 3 decimal places.

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

Question 31

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 32

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?

A)
B)
C) 7
D)
E)

Question 33

Solve for x: . Round to 3 decimal places.

A) 0.663
B) 1.362
C) 3.663
D) -1.362
E) no solution

Question 34

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 35

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Question 36

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.

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

Question 37

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

A) -0.154
B) 0.323
C) -0.355
D) 3.093
E) 0.390

Question 38

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

A) 76.822
B) 136.659
C) 451.920
D) 163.610
E) 38.606

Question 39

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

A) 0.402
B) 2.485
C) 9.411
D) 4.836
E) 2.100

Question 40

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

A)
B)
C)
D)
E)

Question 41

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

A)
B)
C)
D)
E) 7

Question 42

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 43

Simplify the expression .

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

Question 44

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

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

Question 45

Solve for x: . Round to 3 decimal places.

A) 1.362
B) -1.362
C) 1.517
D) 0.517
E) no solution

Question 46

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

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

Question 47

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 48

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) 0.88 g
D) 4.39 g
E) 5.00 g

Question 49

Evaluate the function at . Round to 3 decimal places.

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

Question 50

Find the exact value of without using a calculator.

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

Question 51

Rewrite the logarithmic equation in exponential form.

A)
B)
C)
D)
E)

Question 52

Rewrite the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 53

Find the exact value of without using a calculator.

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

Question 54

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 55

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 56

Identify the x-intercept of the function .

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

Question 57

An initial investment of $6000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?

A) 9.90 years
B) 1 year
C) 10.29 years
D) 10.90 years
E) 9.29 years

Question 58

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

A) 2
B)
C)
D)
E)

Question 59

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

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

Question 60

Write the exponential equation in logarithmic form.

A)
B)
C)
D)
E)

Question 61

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 62

Graph the function using translations.

A)
B)
C)
D)

Question 63

Find the exact value of without using a calculator.

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

Question 64

Find the value of b that would cause the graph of y = b^x to look like the graph indicated.

A)
B)
C)
D)
E)

Question 65

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

A)
B)
C)
D)
E)

Question 66

Find the exact value of without using a calculator.

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

Question 67

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

A)
B)
C)
D)
E) 2

Question 68

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

Question 69

Graph the function.

A)
B)
C)
D)

Question 70

Rewrite the logarithm in terms of the natural logarithm.

A)
B)
C)
D)
E)

Question 71

Simplify the expression .

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

Question 72

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)
D)
E) 7

Question 73

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

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

Question 74

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

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

Question 75

Solve for x: . Round to 3 decimal places.

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

Question 76

Simplify the expression .

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

Question 77

Identify the graph of the function.

A)
B)
C)
D)
E)

Question 78

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)

Question 79

Graph the exponential function.

A)
B)
C)
D)

Question 80

Condense the expression to the logarithm of a single term.

A)
B)
C)
D)
E)