Deck 5: Exponential and Logarithmic Functions

Question 1

In 2002 the population of Stony Creek was 6500. Their population increases by 0.5% per year. What is the expected population in Stony Creek in 2009? Round your answer to the nearest whole number.

A) 6732
B) 215,250
C) 6533
D) 232

Answer 1

6732

Question 2

In 2001, the population of Pleasantville was 53,500. Their population increases by 2.6% per year. What is the expected population of Pleasantville in 2018? Round your answer to the nearest whole number.

A) 126,176
B) 54,891
C) 83,236
D) 29,736

Answer 2

83,236

Question 3

In 2001 the population of Mountainville was 9,800. Their population increases by 0.24% per year. What is the expected population of Mountainville in 2007? Round your answer to the nearest whole number.

Answer 3

9,942

Question 4

Phytoplankton are microscopic plants that live in the ocean. Phytoplankton grow abundantly in oceans around the world and are the foundation of the marine food chain. One variety of phytoplankton growing in Arctic waters is increasing at a rate of 17% per month. If it is estimated that there are 80 million in the water, how many will there be in 8 months? Utilize formula where N represents the population of phytoplankton. Round to the nearest million.

A) 1833 millions
B) 312 millions
C) 10,880 millions
D) 1510 millions

Question 5

An cherry pie is taken out of the oven with an internal temperature of 338°F. It is placed on a rack in a room with a temperature of 78°F. After 18 minutes, the temperature of the pie is 225°F. What will be the temperature of the pie 20 minutes after coming out of the oven? Round to one decimal place.

A) 216.0°F
B) 215.1°F
C) 567.9°F
D) 343.6°F

Question 6

At 1 P.M. a body is found in a park. The police measure the body's temperature to be 84°F. At . the medical examiner arrives and determines the temperature to be 80°F. Assuming the temperature of the park was constant at 59°F, how long has the victim been dead? (Normal body temperature is 98.6°F.) Round to one decimal place.

A) 10.6 hours before 5 P.M.
B) 4.6 hours before 1 P.M.
C) 10.6 hours before 1 P.M.
D) 24.3 hours before 1 P.M.

Question 7

Carbon-14 has a half-life of 5730 years. How long will it take 15 grams of carbon-14 to be reduced to 12.5 grams? Round to the nearest year.

A) 655 years
B) 3470 years
C) 1507 years
D) 14,812 years

Question 8

Victor just graduated from law school owing $75,000 in student loans. The annual interest rate is 8.5%. Approximately how many years will it take to pay off her student loan if she makes a monthly payment of $690? Round to the nearest year.

Question 9

Match the function with the graph and the model name.

A) Logistic

B) Logistic

C) Logistic

D) Logistic

Question 10

Match the graph and the model name with the function.
Exponential decay

A)
B)
C)
D)

Question 11

Does the graph shown display exponential growth or decay?

Question 12

Find the time it will take to pay off a credit card with a balance of $12,300.00 and interest rate of 13.1% if the monthly payment is $450. Express the answer as years to the nearest 2 decimal places.

Question 13

Solve the exponential equation exactly for x.

A) 3/2
B) 217/2
C) 1
D) 2

Question 14

Solve the exponential equation exactly for x.

A) 1/2
B) 2
C) 5
D) 1/5

Question 15

Solve the exponential equation exactly for x.

A) -2
B) 1
C) 3
D) -1

Question 16

Solve the exponential equation exactly for x.

A) 2
B) -4
C) 4
D) 2, -2

Question 17

Solve the exponential equation exactly for x.

A) -4
B) -4, 4
C) 2
D) -2, 2

Question 18

Solve the exponential equation. Round your answer to two decimal places.

A) 1.00
B) 1.08
C) 2.80
D) 0.71

Question 19

Solve the exponential equation. Round your answer to two decimal places.

A) 0.90
B) 0.78
C) 3.50
D) 0.34

Question 20

Solve the logarithmic equation exactly.

A) 5.5
B) 7
C) 22
D) 6

Question 21

Solve the logarithmic equation exactly.

A)
B)
C)
D) 9995

Question 22

Solve the logarithmic equation exactly.

A) -5
B)
C) -
D) no solution

Question 23

Solve the logarithmic equation. Round your answer to three decimal places.

A) 0.833, - 0.833
B) 10.000
C) 2.718, -2.718
D) 2.565, -2.565

Question 24

Solve the logarithmic equation. Round your answer to three decimal places.
Ln(5x) = 2

A) 2.389
B) 1.316
C) 0.400
D) 1.478

Question 25

Solve the logarithmic equation. Round your answer to three decimal places.

A) -0.25
B) -6.01
C) -6.209
D) -6

Question 26

Solve the exponential equation exactly for x.

Question 27

Solve the exponential equation. Round your answer to three decimal places.

Question 28

Solve the logarithmic equation exactly.
log(2x - 18) = 1

Question 29

Solve the exponential equation. Make sure to isolate the base to a power first. Round your answer to three decimal places.

A) 0.571
B) -0.560
C) 1.000
D) 0.000

Question 30

Solve the exponential equation. Make sure to isolate the base to a power first. Round your answer to three decimal places.

A) 2.031
B) 7.625
C) 2.000
D) 0.693

Question 31

Solve the logarithmic equation. Round your answer to three decimal places.

A) 15.203, -7.223
B) -7.223
C) 15.203
D) 7.391

Question 32

If money is invested in a savings account earning 4.5% interest compounded yearly, how many years will pass until the money doubles?

A) 15.75
B) 0.41
C) 0.66
D) 15.40

Question 33

Solve the exponential equation. Round your answer to two decimal places.

Question 34

Solve the logarithmic equation. Round the answer to two decimal places if necessary.

Question 35

Solve the logarithmic equation.

Question 36

If a seismologist records the energy of P waves as 4.7 × joules and the energy of S waves as what is the total energy? What would the combined effect be on the Richter scale?

A)
B)
C)
D)

Question 37

A city experienced a major earthquake. The energy released measured Calculate the magnitude of the earthquake using the Richter scale.

A) 10.0
B) 6.7
C) 15.4
D) 12.6

Question 38

A substance has an approximate hydrogen ion concentration of about . Calculate its pH value.

A) 8.0
B) 16.2
C) -8.0
D) 74.5

Question 39

Use the properties of logarithms to simplify the expression.

A) 63
B) 1
C) 0
D) not defined

Question 40

Use the properties of logarithms to simplify the expression.

A) -2 ln 4
B) 16
C) 1/16
D) -8

Question 41

Use the properties of logarithms to simplify the expression.

A) 256
B) 16
C) 1/256
D) 81

Question 42

Use the properties of logarithms to simplify the expression.

A) 5
B) 125
C) 3
D) 1/3

Question 43

Use the properties of logarithms to simplify the expression.

A) 2
B) 1/2
C) 1
D) 0

Question 44

Write the expression as a sum or difference of logarithms.

A)
B)
C)
D)

Question 45

Write the expression as a sum or difference of logarithms.

A)
B)
C)
D)

Question 46

Write the expression as a sum or difference of logarithms.

A)
B)
C)
D)

Question 47

Write the expression as a sum or difference of logarithms.

A)
B)
C)
D)

Question 48

Write the expression as a single logarithm.
5log u + 6log v

A) log
B) log
C) log (uv)
D) log

Question 49

Write the expression as a single logarithm.
5log u - log v - 9log z

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

Question 50

Write the expression as a single logarithm.

A) ln
B) ln
C) ln
D)

Question 51

Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places.

A) 3.52
B) 1.53
C) 2.68
D) 0.37

Question 52

Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places.

A) 1.67
B) 0.60
C) 5.20
D) 2.26

Question 53

Use the properties of logarithms to simplify the expression.

Question 54

Write the expression as a single logarithm.
ln(x + 9) - 5ln(x - 4)

Question 55

Evaluate the logarithm using the change of base formula. Round your answer to two decimal places.

Question 56

If a seismologist records the energy of P waves as 4.1 × joules and the energy of S waves as what is the total energy? What would the combined effect be on the Richter scale?

A)
B)
C)
D)

Question 57

Use the properties of logarithms to simplify the expression.

A) 3
B) 1/3
C) 1
D) 0

Question 58

Evaluate the logarithm using the change of base formula. Round your answer to two decimal places.

Question 59

Write the logarithmic equation in its equivalent exponential form.

A)
B)

C)
D)

Question 60

Write the logarithmic equation in its equivalent exponential form.

A)
B)
C)
D)

Question 61

Write the logarithmic equation in its equivalent exponential form.
Log 1000 = 3

A)
B)
C)
D)

Question 62

Write the logarithmic equation in its equivalent exponential form.
Log 0.01 = -2

A)
B)
C)
D)

Question 63

Write the exponential equation in its equivalent logarithmic form.

A) ln 125 = 5
B)
C)
D)

Question 64

Write the exponential equation in its equivalent logarithmic form.

A) ln 625 = 4
B)
C)
D) log 625 = 4

Question 65

Write the exponential equation in its equivalent logarithmic form.

A)
B)
C)
D)

Question 66

Evaluate the logarithm exactly.

A) 1
B) 37
C) 0
D) undefined

Question 67

Approximate the common logarithm using the calculator. Round your answer to two decimal places.
Log 838

A) 2.92
B) 8380
C) 6.73
D) 2277.92

Question 68

Approximate the common logarithm using the calculator. Round your answer to two decimal places.
Log 0.0101

A) -4.60
B) -2.00
C) 0.03
D) 0.101

Question 69

Approximate the natural logarithm using a calculator. Round your answer to two decimal places.
Ln 33

A) 1.52
B) 89.70
C) 3.50
D) 330

Question 70

Approximate the natural logarithm using a calculator. Round your answer to two decimal places.
Ln 0.0084

A) -2.08
B) 0.08
C) 0.02
D) -4.78

Question 71

State the domain of the logarithm function f (x) = (10 - x) in interval notation.

A) (10, ?)
B) (-?, 10)
C) (-?, 10]
D) (0, ?)

Question 72

State the domain of the logarithm function f (x) = .

A) (-?, ?)
B) (-3, 3)
C) (0, ?)
D) (-?, -3) ? (-3, ?)

Question 73

State the domain of the logarithm function f (x) =

A) (0, ?)
B) [- 4, 4]
C) (- 4, 4)
D) (-?, 4) ? ( 4, ?)

Question 74

Write the logarithmic equation in its equivalent exponential form.

Question 75

State the domain of the logarithmic function f (x) = (47 - x) in interval notation.

Question 76

Write the exponential equation in its equivalent logarithmic form.

Question 77

Graph the logarithmic function.

Question 78

Graph the logarithmic function using transformation techniques.

Question 79

Match the graph with the logarithmic function.

A)

B)

C)

D)

Question 80

Match the graph to the logarithmic function.

A)
B)
C)
D)