Deck 3: Exponential and Logarithmic Functions

Question 1

In 2002 the population of Stony Creek was 7,500. Their population increases by 1.5% per year. What is the expected population in Stony Creek in 2018? Round your answer to the nearest whole number.

A) 9,534
B) 2,e14
C) 7,613
D) 2,034

Answer 1

9,534

Question 2

In 2001, the population of Pleasantville was 62,500. Their population increases by 1.4% per year. What is the expected population of Pleasantville in 2025? Round your answer to the nearest whole number.

A) 120,683
B) 63,375
C) 87,459
D) 24,959

Answer 2

87,459

Question 3

In 2001 the population of Mountainville was 6,900. Their population increases by 0.27% per year. What is the expected population of Mountainville in 2015? Round your answer to the nearest whole number.

Answer 3

7,166

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 tropical waters is increasing at a rate of 8% per month. If it is estimated that there are 80 million in the water, how many will there be in 7 months? Utilize formula N = N₀e^rt, where N represents the population of phytoplankton. Round to the nearest million.

A) 290 millions
B) 140 millions
C) 4,480 millions
D) 20 millions

Question 5

An cherry pie is taken out of the oven with an internal temperature of 348ºF. It is placed on a rack in a room with a temperature of 73ºF. After 21 minutes, the temperature of the pie is 240ºF. What will be the temperature of the pie 35 minutes after coming out of the oven? Round to one decimal place.

A) 192.8ºF
B) 187.3ºF
C) 704.5ºF
D) 356.7ºF

Question 6

At 5 A.M. a body is found in a park. The police measure the body's temperature to be 90ºF. At 6 A.M. the medical examiner arrives and determines the temperature to be 86ºF. Assuming the temperature of the park was constant at 70ºF, how long has the victim been dead? (Normal body temperature is 98.6ºF.) Round to one decimal place.

A) 1.6 hours before 6 A.M.
B) 0.7 hours before 5 A.M.
C) 1.6 hours before 5 A.M.
D) 3.7 hours before 5 A.M.

Question 7

Carbon-14 has a half-life of 5730 years. How long will it take 11.5 grams of carbon-14 to be reduced to 6.5 grams? Round to the nearest year.

A) 2,048 years
B) 10,860 years
C) 4,716 years
D) 6,885 years

Question 8

Josh just graduated from medical school owing $51,000 in student loans. The annual interest rate is 7%. Approximately how many years will it take to pay off her student loan if she makes a monthly payment of $750? Round to the nearest year.

Question 9

Match the function with the graph and the model name.

A) Logarithmic
B) Logarithmic
C) Logarithmic
D) Logarithmic

Question 10

Match the function with the graph and the model name.
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 $10800 and interest rate of 17.1% 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.
4 ^{2x + 1} = 262144

A)
B) -4
C) 4
D)

Question 14

Solve the exponential equation exactly for x.
81^x = 3

A) 1/4
B) 4
C) 27
D) 1/27

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.
3 ^{4x - 1} = 24

A) 0.77
B) 0.97
C) 2.25
D) 0.55

Question 19

Solve the exponential equation. Round your answer to two decimal places.
2(10^4x) = 30

A) 1.23
B) 0.68
C) 3.75
D) 0.29

Question 20

Solve the logarithmic equation exactly.

A) 6.5
B) 7
C) 8
D) 2

Question 21

Solve the logarithmic equation exactly.

A)
B)
C)
D) 2

Question 22

Solve the logarithmic equation exactly.

A) -2
B)3
C) no solution
D)

Question 23

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

A) 1.269, -1.269
B) 316.228
C) 12.182, -12.182
D) 8.912, -8.912

Question 24

Solve the logarithmic equation. Round your answer to three decimal places.
Ln (4x) = 3

A) 16.086
B) 4.953
C) 0.750
D) 5.021

Question 25

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

A) 0.333
B) -3.048
C) -3.237
D) -3.001

Question 26

Solve the exponential equation exactly for x.
3 ^{2x - 2} = 9

Question 27

Solve the exponential equation. Round your answer to three decimal places.
5(10 ^3x) = 13

Question 28

Solve the logarithmic equation exactly.
log(2x - 8) = 3

Question 29

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

A) 0.359
B) -1.025
C) 1.859
D) 0.620

Question 30

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

A) 0.916454
B) 8.250
C) 9.000
D) 0.954243

Question 31

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

A) 8.711, -5.511
B) -5.511
C) 8.711
D) 3.827

Question 32

If money is invested in a savings account earning 5.3% interest compounded daily, how many years will pass until the money doubles?

A) 13.08
B) 0.13
C) 0.00
D) 13.08.

Question 33

The magnitude M of an earthquake is measured using the Richter Scale
where M is the magnitude
E is the seismic energy energy released by the earthquake ( in joules)
E₀ is the energy released by a reference earthquake E₀ = 10^4.4 joules
On September 25, 2003, an earthquake that measured
7.0 on the Richter scale shook Hokkaido, Japan. How much energy (joules) did the earthquake emit?

Question 34

If

, then

. Use the property to find the derivative of

Question 35

Write in an equivalent form using the natural logarithm.

Question 36

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

Question 37

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

Question 38

Solve the logarithmic equation.

Question 39

27. If a seismologist records the energy of P waves as 4.7 x 10¹² joules and the energy of S waves as 3.4 x 10⁹ joules, what is the total energy? What would the combined effect be on the Richter scale?

A) Total energy is 4.7 x 10¹² joules and 5.5 on the Richter scale
B) Total energy is 8.1 x 10^21.0 joules and 5.5 on the Richter scale
C) Total energy is 1.3 x 10³ joules and 5.5 on the Richter scale
D) Total energy is 1.6 x 10^22.0 joules and 5.5 on the Richter scale

Question 40

28. A city experienced a major earthquake. The energy released measured 4.9 x 10¹⁵ joules. Calculate the magnitude of the earthquake using the Richter scale.

A) 11.3
B) 7.5
C) 17.3
D) 13.4

Question 41

29. A substance has an approximate hydrogen ion concentration of about 4.8 x 10^-3.1 . Calculate its pH value.

A) 3.8
B) 5.6
C) -3.8
D) 2.4

Question 42

Use the properties of logarithms to simplify the expression.
Log ₄₄ 44

A) 44
B) 1
C) 0
D) undefined

Question 43

Use the properties of logarithms to simplify the expression.
E^-4ln6

A) -4 ln 6
B) 1296
C) 1/1296
D) -24

Question 44

Use the properties of logarithms to simplify the expression.

A) 81
B) 12
C) 1/81
D) 256

Question 45

Use the properties of logarithms to simplify the experssion.
Log ₃ 81

A) 3
B) 81
C) 4
D) 1/4

Question 46

Use the properties of logarithms to simplify the expression.

A) 18
B) 1/18
C) 1
D) 0

Question 47

Write the expression as a sum or difference of logarithms.
Log_b (x²y^-4)

A) 2log_b x + 4log_b y
B) 2log_b x - 4log_b y
C) -4log_b x - 2log_b y
D) -8log_b(xy)

Question 48

Write the expression as a sum or difference of logarithms.

A) 7log_b x + log_b y - 3log_bz
B) 7log_b x + log_b y + 3log_bz
C) 7log_b x - log_b y - 3log_bz
D)

Question 49

Write the expression as a sum or difference of logarithms.

A)
B)
C)
D)

Question 50

Write the expression as a sum or difference of logarithms.

A)
B)
C)
D)

Question 51

Write the expression as a single logarithm.
5log u + 2log v

A) log (u⁵v²)
B) log (u⁵ + v²)
C) log (uv)
D) log (uv)¹⁰

Question 52

Write the expression as a single logarithm.
4log u - log v - 6log z

A)
B)
C)
D)

Question 53

Write the expression as a single logarithm.

A)
B)
C)
D)

Question 54

Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places.
Log _6.4 12.6

A) 4.39
B) 1.91
C) 1.36
D) 0.73

Question 55

Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places.
Log ₃ 13

A) 2.33
B) 0.43
C) 3.66
D) 1.59

Question 56

Use the properties of logarithms to simplify the expression.

Question 57

Write the expression as a single logarithm.
ln(x + 8) - 7ln(x - 5)

Question 58

Evaluate the logarithm using the change of base formula. Round your answer to two decimal places.
log_1.3 6.2

Question 59

If a seismologist records the energy of P waves as 4.7 x 10¹⁰ joules and the energy of S waves as 8.3 x 10⁷ joules, what is the total energy? What would the combined effect be on the Richter scale?

A) Total energy is 4.7 x 10¹⁰ joules and 4.2 on the Richter scale
B) Total energy is 1.3 x 10¹⁸joules and 9.1 on the Richter scale
C) Total energy is 3.7 x 10³joules and -0.6 on the Richter scale
D) Total energy is 3.8 x 10¹⁸joules and 9.5 on the Richter scale

Question 60

The pH scale measures how acid or base a substance is. pH is defined as the negative logarithm of the hydrogen ion activity in an aqueous solution a_h. Thus if a_h = 0.01, then the pH = -log 0.01 = 2. Determine the pH of a liquid with a_h = 0.00398107. Round your answer to the nearest hundredth.

Question 61

Use the properties of logarithms to simplify the expression.

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

Question 62

Evaluate the logarithm using the change of base formula. Round your answer to two decimal places.
log₄ 89

Question 63

Write the logarithmic equation in its equivalent exponential form.

A) 16 ^-4 = 1/2
B) (1/2)^-4 = 16
C) 2 ⁴ = 16
D) 2 ^-4 = 16

Question 64

Write the logarithmic equation in its equivalent exponential form.

A) 2 ¹⁶ = 4
B) 2 ⁴ = 16
C) 4 ² = 16
D) 16 ^1/2 = 4

Question 65

Write the logarithmic equation in its equivalent exponential form.
Log 10,000 = 4

A) 10⁴ = 10,000
B) e⁴ = 10,000
C) 4¹⁰ = 10,000
D) 10,000^1/4 = 10

Question 66

Write the logarithmic equation in its equivalent exponential form.
Log 0.0001 = -4

A) 10⁴ = 0.0001
B) e^-4 = 0.0001
C) 10^-4 = 0.0001
D) 0.0001⁴ = 10

Question 67

Write the exponential equation in its equivalent logarithmic form.
2 = 16^1/4

A) ln 16 = 2
B)
C)
D)

Question 68

Write the exponential equation in its equivalent logarithmic form.
5 ³ = 125

A) ln 125 = 3
B)
C)
D) log 125 = 3

Question 69

Write the exponential equation in its equivalent logarithmic form.

A) log_3/5 (81/625) = 4
B) log_81/625 (3/5) = 4
C) log (81/625) = 4
D) ln (81/625) = 4

Question 70

Evaluate the logarithm exactly.
Log₄ 1

A) 1
B) 4
C) 0
D) undefined

Question 71

Approximate the common logarithm using the calculator. Round your answer to two decimal places.
Log 332

A) 2.52
B) 3,320
C) 5.81
D) 902.47

Question 72

Approximate the common logarithm using the calculator. Round your answer to two decimal places.
Log 0.0051

A) -5.28
B) -2.29
C) 0.01
D) 0.051

Question 73

Approximate the natural logarithm using a calculator. Round your answer to two decimal places.
Ln 23

A) 1.36
B) 62.52
C) 3.14
D) 230

Question 74

Approximate the natural logarithm using a calculator. Round your answer to two decimal places.
Ln 0.001

A) -3.00
B) 0.01
C) 0.00
D) -6.91

Question 75

State the domain of the logarithm function

In interval notation.

A) (5, $\infty$ )
B) (- $\infty$ , 5)
C) (- $\infty$ , 5]
D) (0, $\infty$ )

Question 76

State the domain of the logarithm function f(x) = log₆ (x² + 7).

A) (-, $\infty$ )
B) (-7, 7)
C) (0, $\infty$ )
D) (- $\infty$ , -7) $\cup$ ( -7 , $\infty$ )

Question 77

State the domain of the logarithm function f(x) = log₂ (100 - x²).

A) (-10, 10)
B) [-10, 10]
C) (0, $\infty$ )
D) (- $\infty$ , 10) $\cup$ (10 , $\infty$ )

Question 78

Write the logarithmic equation in its equivalent exponential form.
log₆ 369.74 = 3.3

Question 79

State the domain of the logarithmic function f(x) = log₉ (52 - x) in interval notation.

Question 80

Write the exponential equation in its equivalent logarithmic form.
4 ^4.9 = 891.44