Deck 4: Systems of Linear Equations

Question 1

The value of is 13.05.

Answer 1

False

Question 2

Find the logarithm of .

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

Answer 2

Question 3

Using the definition of the logarithmic function solve .

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

Answer 3

-4

Question 4

Find .

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

Question 5

Which one of the following exponential equations is equivalent to .

A)
B)
C)
D)
E)

Question 6

The number is approximately equal to 2.71828.

Question 7

Question 8

Question 9

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

Question 10

Find the logarithm of .

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

Question 11

Which one of the following exponential equations is equivalent to ?

A)
B)
C)
D)
E)

Question 12

For any the logarithm function is always decreasing.

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

Question 15

Find .

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

Question 16

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

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

Question 17

Using the definition of the logarithmic function solve for .

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

Question 18

Find .

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

Question 19

The value of is .

Question 20

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 21

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

A)
B)
C)
D)
E)

Question 22

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

A)
B)
C)
D)
E)

Question 23

Which one of the following graphs represents the function ?

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

Question 24

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 25

Use the Laws of Exponents to expand the expression .

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

Convert the function to the form .

A)
B)
C)
D)
E)

Question 28

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

A)
B)
C)
D)
E)

Question 29

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 30

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

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

Question 31

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 32

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 33

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

A)
B)
C)
D)
E)

Question 34

Evaluate the expression . Round to the nearest thousandth.

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

Question 35

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 36

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) -3667 mol/L
C) 2928 mol/L
D) 2192 mol/L
E) 1272 mol/L

Question 37

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 38

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 39

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 40

Which one of the following graphs represents the function ?

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

Question 41

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 42

If $49000 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) $50239.13
B) $49000
C) $80292.21
D) $80745.33
E) $51082.58

Question 43

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 44

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) 20942.04
B) 5822.67
C) 20394.45
D) 16022649.18
E) 5375

Question 45

Solve the logarithmic equation for .

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

Question 46

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 47

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

A) 0.217
B) 4.605
C) 273252.194
D) 2.718
E) 2.000

Question 48

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 49

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 17871. 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 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

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 52

If $18000 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) $38626.59
B) $38040.78
C) $38681.90
D) $18000
E) $18828.50

Question 53

If $16000 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 54

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 55

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

A) 10
B) 2
C) 1024
D) 20
E) 100

Question 56

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

A)
B)
C)
D)
E)

Question 57

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 58

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 59

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 60

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 16409. Determine the number of new cases of the H1N1 virus after 9 days. Rounded to the nearest whole number.

A) 24117
B) 57139
C) 18849
D) 8401408
E) 17723

Question 61

Using the graph below determine .

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

Question 62

Use the table of values to solve the system.

A)
B)
C)
D)

Question 63

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

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

Question 64

Use the table of values to solve the system.

A)
B)
C)
D)

Question 65

Find the inverse of .

A)
B)
C)
D)
E)

Question 66

If and determine .

A)
B)
C)
D)
E)

Question 67

Use the table of values to solve the system.

A)
B)
C)
D)

Question 68

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 69

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

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

Question 70

You are choosing between two jobs. Job one pays $10 per hour for 32 hours per week. Job 2 pays $8 per hour plus a commission of 10% of your sales again based on 32 hours per week. At what amount of sales is your weekly pay the same at the two jobs? Let s be your amount of sales and let p be amount of pay. Use the table of values to solve the system.

A) at sales of $100
B) at sales of $300
C) at sales of $640
D) at sales of $700

Question 71

Use the table of values to solve the system.

A)
B)
C)
D)

Question 72

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 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)

Question 75

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 76

Use the table of values to solve the system.

A)
B)
C)
D)

Question 77

If and determine . Round to the nearest tenth.

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

Question 78

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 79

Find the inverse of .

A)
B)
C)
D)
E)

Question 80

Jennifer invests $5100 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 $13000? 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