Deck 4: Logarithmic Functions and Exponential Modela

Question 1

Find .

A) 4
B)
C) 1
D) 10
E) 0

Answer 1

0

Question 2

The number is approximately equal to 2.71828.

Answer 2

True

Question 3

Find .

A) 6
B) 8
C) 262144
D) 48
E) 1

Answer 3

6

Question 4

Using the definition of the logarithmic function, solve for .

A) 6
B) -6
C) 1.6
D) -2
E) 2

Question 5

Which of the following is the correct missing value in the table for the function ?

A)
B)
C) 1
D) -1
E) 5

Question 6

Find the logarithm of .

A) -3
B)
C) 3
D) 10
E)

Question 7

Find the logarithm of .

A) 2
B)
C) 100
D) 8
E) 10

Question 8

Question 9

If , then . Assume that is a one-to-one function.

Question 10

Which one of the following exponential equations is equivalent to .

A)
B)
C)
D)
E)

Question 11

Question 12

Question 13

Using the definition of the logarithmic function, solve for .

A) 0.6
B) 60.0
C) 1.7
D) 60466176
E) 1000000

Question 14

Find the common logarithm of the given value, rounded to the nearest thousandth, of:
The weight of an African Grey parrot: 380 grams.

A) 5.940
B) 380
C) 3.8
D) 10
E) 2.580

Question 15

Which one of the following exponential equations is equivalent to ?

A)
B)
C)
D)
E)

Question 16

Find .

A)
B) -8
C)
D) 390625
E) 8

Question 17

The value of is .

Question 18

The value of is 13.05.

Question 19

For any , the logarithm function is always decreasing.

Question 20

Using the definition of the logarithmic function, solve .

A) 0.0001
B) -4
C) 10
D) 1048576
E) 4

Question 21

Which one of the following is the correct combination of the logarithm in simplified form?

A)
B)
C)
D)
E)

Question 22

If the hydrogen ion concentration of a soil sample is , what is the pH level of the soil?

A) -6.51
B) -14.99
C) 3.10
D) 14.99
E) 6.51

Question 23

Which one of the following is the correct combination of the logarithm in simplified form?

A)
B)
C)
D)
E)

Question 24

Evaluate the expression . Round to the nearest thousandth.

A) -12.000
B) 1.511
C) -0.255
D) -0.328
E) 1.839

Question 25

The initial size of a population is 2700 and it has an instantaneous decay rate of 30% per year. Which one of the following exponential functions model this population where is measured in years?

A)
B)
C)
D)
E)

Question 26

Which one of the following is the correct expansion of the logarithm expression ?

A)
B)
C)
D)
E)

Question 27

If we know the amount of light that is absorbed in a solution, we can calculate the concentration of the substance dissolved in water using a spectrophotometer. For a certain substance the concentration (in moles/liter) is given by the formula , where is the intensity of the incident light and is the intensity of light that emerges. What is the concentration of the substance if the intensity is 45% of ?

A) 952 mol/L
B) -3,667 mol/L
C) 2,928 mol/L
D) 2,192 mol/L
E) 1,272 mol/L

Question 28

The pH of tomatoes is normally in the range of 4.1-4.4. If the pH of tomatoes is too high, nutrient deficiencies and toxicity will occur. Tomatoes from a local grocery store have a pH of 4.2. What is the hydrogen ion concentration for the tomatoes from this store?

A) -4.20e+01
B) 6.31e-05
C) 4.20e+00
D) 1.58e+04
E) 1.50e-02

Question 29

A 3.2-magnitude earthquake hit off the Oregon coast in August 2009. In the same month, an earthquake 4 times as intense struck China. What was the magnitude of the earthquake in China?

A) 12.8
B) 3.2
C) 3.8
D) 4.6
E) 0.5

Question 30

Which one of the following graphs represents the function ?

A)
B)
C)
D) None of these options
E)

Question 31

For the exponential model , what is the instantaneous growth or decay rate.

A) 82.2%
B) 182.2%
C) 2.7%
D) 60%
E) 0.6%

Question 32

Use the Change of Base Formula to evaluate the logarithm . Round to the nearest ten-thousandth.

A) 0.5600
B) 1.6128
C) 1.7859
D) 0.2016
E) 5.1250

Question 33

Fill in the blank.
A magnitude 8 earthquake is _________ times more intense than a magnitude 3 earthquake.

A) 100000
B) 0.00001
C) 10000
D) 1000
E) 5

Question 34

Use the Laws of Exponents to expand the expression .

A)
B)
C)
D)
E)

Question 35

Which one of the following is the correct expansion of the logarithm expression ?

A)
B)
C)
D)
E)

Question 36

Which one of the following is the correct expansion of the logarithm expression ?

A)
B)
C)
D)
E)

Question 37

On August 18, 2009, a 6.3 magnitude earthquake was detected south of the Fiji Islands. On August 23, 2009, a 5.2 magnitude earthquake was detected in the same area. How many times more intense was the August 18th earthquake than the August 23rd earthquake? (Rounded to the nearest hundredth)

A) 1.10
B) 0.08
C) 12.59
D) 4.16
E) 16.28

Question 38

The graph of a logarithmic function is shown below. Find the base .

A)
B) 1
C)
D) 5
E) -5

Question 39

Which one of the following graphs represents the function ?

A)
B)
C)
D) None of these options
E)

Question 40

Convert the function to the form .

A)
B)
C)
D)
E)

Question 41

If $18,000 is invested at an interest rate of 4.5% compounded continuously, what is the amount of the investment after 10 years? Rounded to the nearest hundredth.

A) $38,626.59
B) $38,040.78
C) $38,681.90
D) $18,000
E) $18,828.50

Question 42

If $16,000 is invested at an interest rate of 6% for 25 years, compounded continuously, determine the annual growth rate if the money were compounded quarterly? Rounded to the nearest thousandth of a percent.

A) 0.011%
B) 6.000%
C) 6.184%
D) 0.060%
E) 106.184%

Question 43

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 5 days for several months. As of July 27, 2009, the number of new cases was 16,409. Determine the number of new cases of the H1N1 virus after 9 days. Rounded to the nearest whole number.

A) 24,117
B) 57,139
C) 18,849
D) 8,401,408
E) 17,723

Question 44

Solve the logarithmic equation for . Round to the nearest thousandth.

A) 10
B) 2
C) 1,024
D) 20
E) 100

Question 45

Solve the logarithmic equation for . Round to the nearest ten-thousandth.

A) 0.3333
B) 0.0833
C) -0.25
D) -1
E) -0.75

Question 46

Solve the exponential equation for . Round to the nearest thousandth.

A) 0.604
B) 6.611
C) -0.274
D) 1.604
E) -0.230

Question 47

Solve the exponential equation for . Round to the nearest thousandth.

A) 0.217
B) 4.605
C) 273,252.194
D) 2.718
E) 2.000

Question 48

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 3 days for several months. Determine the daily growth factor for the H1N1 virus (rounded to the nearest thousandths).

A) 8.000
B) 1.732
C) 2.000
D) 1.000
E) 1.260

Question 49

Solve the exponential equation for . Round to the nearest thousandth.

A) 3.054
B) 0.602
C) 1.839
D) 2.882
E) 0.327

Question 50

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 5 days for several months. As of July 27, 2009, the number of new cases was 26116. Which one of the following exponential functions model the growth of this virus?

A)
B)
C)
D)
E)

Question 51

Solve the exponential equation for . Round to the nearest thousandth.

A) 1.946
B) 2.189
C) 12.772
D) -0.043
E) -23.133

Question 52

Using the graph below, determine which one of the following exponential functions models the graph.

A)
B)
C)
D)
E)

Question 53

Solve the logarithmic equation for .

A) 5
B) -5
C) 5.0
D) No solution
E) 0

Question 54

Solve the exponential equation for . Round to the nearest thousandth.

A) -0.924
B) 2.076
C) 2.303
D) 6.576
E) 4.000

Question 55

If $49,000 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 20 years if the money is compounded monthly. Round to the nearest hundredth.

A) $50,239.13
B) $49,000
C) $80,292.21
D) $80,745.33
E) $51,082.58

Question 56

The number of bees in a certain area of Arizona is modeled by the function where is measured in number of weeks. Determine the number of bees after 17 weeks. Rounded to the nearest whole number.

A) 20,942.04
B) 5,822.67
C) 20,394.45
D) 16,022,649.18
E) 5,375

Question 57

On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 5 days for several months. As of July 27, 2009, the number of new cases was 17,871. Determine the instantaneous growth rate for the virus (rounded to the nearest ten-thousandths).

A) 0.3495
B) 0.1386
C) 1.3979
D) 1.1487
E) 0.0602

Question 58

Solve the logarithmic equation for . Round to the nearest hundredth.

A) 24.00
B) No Solution
C) 0.13
D) 0.38
E) -0.63

Question 59

Solve the exponential equation for . Round to the nearest thousandth.

A) 1.100
B) 1.230
C) 1.705
D) 0.813
E) 1.375

Question 60

Solve the logarithmic equation for . Round to the nearest hundredth.

A) 0.24
B) 0.15
C) 4.25
D) 0.29
E) 0.31

Question 61

The graphs of two functions and are given below. Using the graphs, determine .

A) 2
B) 4.8
C) 7.6
D) 15.2
E) -1.6

Question 62

Two functions and are given by the tables below. Determine .

A) 0
B) -1
C) 5
D) 1
E) -2

Question 63

A car dealer advertises a 35% discount on all cars available in the current inventory. In addition, the car dealer offers a $1800 rebate on the purchase of a new care. The dealer decides to apply the rebate first and then award the 35% discount afterwards. Let represent the sticker price of the new car. Which one of the following functions model the final price of the car once the rebate and discount have been awarded?

A)
B)
C)
D)
E)

Question 64

Two functions and are given by the tables below. Determine .

A) 5
B) 3
C) 4
D) 1
E) 2

Question 65

If and , determine . Round to the nearest tenth.

A) 2
B) 20.1
C) -20.1
D) 7.4
E) -15.1

Question 66

Find the inverse of .

A)
B)
C)
D)
E)

Question 67

If and , determine .

A)
B)
C)
D)
E)

Question 68

The mass of bacteria in a Petri dish is 56 micrograms. After 3 hours, the bacteria's mass as increased to 164 micrograms. How long will it take for the population to quadruple?

A) 1.3 hours
B) 3.9 hours
C) 0.3 hours
D) 2.9 hours
E) 1.4 hours

Question 69

Find the inverse of .

A)
B)
C)
D)
E)

Question 70

Jennifer invests $5,100 in a saving certificate with an interest rate of 4.25% per year, compounded monthly. How long will it take for her investment to grow to $13,000? Round to the nearest tenth.

A) 1.9 years
B) 4.3 years
C) 215.6 years
D) 22.1 years
E) 211.5 years

Question 71

The half-life of Radon-222 is 3.8 days. A 32-gram sample of Radon-222 is monitored for one day. How long will it take for the sample to be 24% of the initial amount? (rounded to the nearest hundredths)?

A) 0.1 days
B) 7.8 days
C) 3.8 days
D) 1.8 days
E) 0.5 days

Question 72

Using the graph below, determine .

A) 0.33
B) 0.05
C) 120
D) 19.84
E) 3

Question 73

Find the inverse of .

A)
B)
C)
D)
E)

Question 74

The mass of bacteria in a Petri dish is 30 micrograms. After 3 hours, the bacteria s mass as increased to 141 micrograms. Which one of the following exponential functions model the bacteria s growth, where is measured in hours.

A)
B)
C)
D)
E)