Deck 3: Linear Equations With Two Variables

Question 1

In 1990 a town's population was 22104. In 1998 the town's population increased to 31132. Assuming that the population increased exponentially the population in 1994 was 26618.

Answer 1

False

Question 2

In 1990 a town's population was 21435. In 1998 the town's population increased to 32054. Assuming that the population increased exponentially the population in 1982 was 14334.

Answer 2

True

Question 3

The horizontal asymptote of the graph is .

Answer 3

True

Question 4

In 1990 a town s population was 24127. In 1998 the town s population increased to 33887. Assuming that the population increased exponentially from 1990-1998 this data can be modeled by where t is the number of years since 1990.

Question 5

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. True or false? The function f(t) grows linearly.

Question 6

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. True or false? The population of f(t) after 4 years exceeds the carrying capacity for the logistic function.

Question 7

Data from local gas stations have revealed that gas prices decreased exponentially each week in late 2008. However there is debate over which model accurately describes the falling gas prices. Jim believes that the correct model for gas prices after x weeks is while April believes the model should be . What comparisons can be made about the two different models?

A) The gas prices decreased at a rate of 76% every week as opposed to 94% every week.
B) The gas prices decreased at a rate of 24% every week as opposed to 6% every week.
C) The price of the gas is $0.18 less than it was before.
D) The initial gas price decreased.
E) After x weeks the gas price is 0.76 times as much as the initial gas price instead of 0.94 times as much.

Question 8

The table can be modeled by where t represents the number of days since Monday.

Question 9

The average rate of change for the increase in bees per day for time 0 to 2 days is 4.02.

Question 10

The percent rate of change for the increase in bees per day for time 0 to 2 days is 7.46%.

Question 11

The number of people infected with the H1N1 virus as a function of time (in months) was originally modeled by . Based on new data this model was updated to . What conclusions can be made based on the revised model?

A) After t months the number of people infected with the virus is now 1.6 times as much as the initial value instead of 1.2 times as much.
B) The number of people infected increases by 60% every month rather than 20% every month.
C) There are 0.4 additional people infected with the virus.
D) The initial number of people infected with the virus is now 1.6 instead of 1.2.
E) The growth rate of the virus increased from 120% to 160%.

Question 12

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. True or false? The function g(t) grows logistically.

Question 13

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. True or false? The population of g(t) after 4 years exceeds the carrying capacity for the logistic function.

Question 14

Which one of the following scenarios does NOT describe exponential growth?

A) A population increases by 8.5% every year.
B) A population doubles every 5 years.
C) A population grew by a factor of 1.49 every 5 years.
D) A population in a certain year was 104% of the population the previous year.
E) A population increases by 1600 people every year.

Question 15

The growth factor is 1.061.

Question 16

The table represents data for an exponential function.

Question 17

In 1990 a town's population was 21354. In 1998 the town's population increased to 29012. Assuming that the population increased exponentially the one-year growth factor is 1.039.

Question 18

The function is a model for a population A where t is measured in years. The function is a model for a population B where t is measured in years. True or false? The initial population of f(t) is equal to the initial population of g(t) .

Question 19

Which one of the following scenarios does not describe exponential decay?

A) A radioactive substance decayed by 53 grams every 3 hours.
B) A radioactive substance decreases by half every hour.
C) A radioactive substance in a certain hour was 81% of the population the previous hour.
D) The half-life of a radioactive substance is 10.9 hours.
E) A radioactive substance decreases by 11% every hour.

Question 20

In 1990 a town's population was 24382. In 1998 the town's population increased to 30608. Assuming that the population increased exponentially the population in 2006 was 38424.

Question 21

The model describes the amount of a radioactive substance (in grams) remaining after t hours. Which one of the following written statements best describes this population?

A) The amount of radioactive substance decreases by 24% each hour.
B) The amount of radioactive substance increases by 76% each hour.
C) The amount of radioactive substance decreases by 0.76 each hour.
D) The amount of radioactive substance increases by 24% each hour.
E) The amount of radioactive substance decreases by 76% each hour.

Question 22

The amount of caffeine (in milligrams) left in an adult body t hours after drinking a 16 oz. coke is modeled by . What is the decay factor?

A) 0.72
B) 28
C) 72
D) 155
E) 0.28

Question 23

The number of ants in a colony at time t (in days) is modeled by . How many ants will be in the colony after 6 days (rounded to the nearest integer)?

A) 759
B) 449
C) 10461
D) 23
E) 4553

Question 24

The population of Smallville at time t (in years) is modeled by . What is the initial population of Smallville?

A) 40
B) 0.4
C) 2000
D) 1.4
E) 2800

Question 25

The population of Smallville at time t (in years) is modeled by . What is the growth rate (in percentage form)?

A) 30%
B) 130%
C) 1.3%
D) 3%
E) 0.3%

Question 26

The revenue (in millions) of a struggling corporation at time t (in months) is modeled by . What is the one-year decay factor for corporation s revenue (rounded to the nearest hundredth)?

A) 16.29
B) 0.99
C) 0.32
D) 0.91
E) 10.92

Question 27

The number of tourists in a small town at time t (in years) is modeled by . What is the decay rate (in percentage form)?

A) 65%
B) 135%
C) 0.65%
D) 0.35%
E) 35%

Question 28

The model describes the amount of Cesium-137 remaining after t years. Which one of the following written statements best describes the behavior of Cesium-137?

A) The amount of radioactive substance decreases by half every years.
B) The amount of radioactive substance increases by half every year.
C) The amount of radioactive substance increases by half every years.
D) The amount of radioactive substance decreases by half every 79 years.
E) The amount of radioactive substance decreases by half every year.

Question 29

The number of tourists in a small town at time t (in years) is modeled by . What is the initial number of tourists?

A) 5
B) 2400
C) 2280
D) 95
E) 0.95

Question 30

The amount of caffeine (in milligrams) left in an adult body t hours after drinking a 16 oz. coke is modeled by . What is the initial population?

A) 127.82
B) 0.83
C) 154
D) 0.17
E) 1

Question 31

The revenue (in millions) of a struggling corporation at time t (in months) is modeled by . What will the corporation s revenue be after 7 months (rounded to the nearest hundredth)?

A) $85.11 million
B) $18.07 million
C) $12.16 million
D) $0.76 million
E) $19.30 million

Question 32

The amount of caffeine (in milligrams) left in an adult body t hours after drinking a 16 oz. coke is modeled by . What is the decay rate (in percentage form)?

A) 23%
B) 0.23%
C) 1.77%
D) 77%
E) 0.77%

Question 33

The number of tourists in a small town at time t (in years) is modeled by . What is the decay factor?

A) 95
B) 0.05
C) 5
D) 0.95
E) 250

Question 34

The model describes the amount of bacteria in a Petri dish after t hours. Which one of the following written statements best describes this population?

A) The amount of bacteria decreases by 17% each hour.
B) The amount of bacteria increases by 117% each hour.
C) The amount of bacteria decreases by 117% each hour.
D) The amount of bacteria increases by 17% each hour.
E) The amount of bacteria increases by 1.17% each hour.

Question 35

A town starts with 100 people and grows by 9% per year with x representing the number of years. Which of the following functions model this behavior?

A)
B)
C)
D)
E)

Question 36

The model describes the population of Town A. Which one of the following written statements best describes this population?

A) The population of Town A increases by 167% per year.
B) The population of Town A increases by 67% per year.
C) The population of Town A increases by 67 people per year.
D) The initial population of Town A increases by 1.67% per year.
E) The population of Town A increases by 167 people per year.

Question 37

The population of Smallville at time t (in years) is modeled by . What is the growth factor?

A) 1.8
B) 8
C) 180
D) 80
E) 0.8

Question 38

A town starts with 200 people and declines by 28% per year with x representing the number of years. Which of the following functions model this behavior?

A)
B)
C)
D)
E)

Question 39

The number of bacteria present in a Petri dish at time t (in minutes) is modeled by . Which one of the following models the population for a one-hour growth factor?

A)
B)
C)
D)
E)

Question 40

The number of ants in a colony at time t (in days) is modeled by . What is the one-week growth factor for the number of ants (rounded to the nearest hundredth)?

A) 8.75
B) 4.77
C) 1.03
D) 0.25
E) 0.18

Question 41

The value of an investment doubles every 32 months. If the investment starts with $3700 how much money is in the investment after 3 months (rounded to the nearest hundredth)?

A) $3700.00
B) $3781.02
C) $7400.00
D) $3948.42
E) $4661.71

Question 42

The number of cell phone users at time t (in years) is modeled by . Which one of the following models the number of cell phone users for a one-month growth factor?

A)
B)
C)
D)
E)

Question 43

A region in the Arizona desert has 351 rabbits and after 3 months there are 896 rabbits. Assuming that the number of rabbits grows exponentially which of the following is the 3-month growth factor (rounded to the nearest tenth)?

A) 181.7
B) 2.6
C) 0.4
D) 16.6
E) 1.4

Question 44

The cash flow (in millions) of a business at time t (in months) is modeled by . What will the cash flow be after 3 years (round to the nearest ten-thousand)?

A) $4.05 million
B) $20.27 million
C) $6.29 million
D) $3.68 million
E) $3.54 million

Question 45

The model describes the amount of Krypton-91 remaining after x minutes. Which one of the following written statements best describes the behavior of Krypton-91?

A) The amount of Krypton-91 decays by half every 4 seconds.
B) The amount of Krypton-91 decays by half every minutes.
C) The amount of Krypton-91 decays by half every 4 minutes.
D) The amount of Krypton-91 decays by half every seconds.
E) The amount of Krypton-91 decays by half every 1 minute.

Question 46

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. What is the 8000-meter decay factor for the atmospheric pressure (rounded to the nearest thousandth)?

A) 0.376
B) 0.885
C) 0.985
D) 0.998
E) 0.115

Question 47

The half-life of Iodine-135 is 8 days. A 121-gram sample of Iodine-135 is monitored for one month. Assuming there are 30 days in the month how many grams of Iodine-135 are left after 1 month (rounded to the nearest hundredths)?

A) 0.47
B) 8.99
C) 110.96
D) 60.50
E) 100.58

Question 48

Morphine is administered to a patient intravenously with an initial amount of 12 mg. About 35.2% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body for 1-minute periods of time?

A)
B)
C)
D)
E)

Question 49

The half-life of Radon-222 is 3.8 days. A 46-gram sample of Radon-222 is monitored for one day. How many grams of Radon-222 are left after 16 hours (rounded to the nearest hundredths)?

A) 46.00
B) 2.48
C) 45.65
D) 40.73
E) 28.98

Question 50

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. Which one of the following models the atmospheric pressure for 700-meter increases in elevation?

A)
B)
C)
D)
E)

Question 51

The value of an investment at time t (in months) is modeled by . What is the one-week growth factor for the value of the investment (rounded to the nearest ten-thousandths)?

A) 1.0572
B) 1.0140
C) 0.2535
D) 4.0560
E) 1.0035

Question 52

A bacterial infection starts with 92 bacteria with the bacteria count doubling every 6-hour time period. Which of the following exponential growth models represent the number of bacteria x hours after infection?

A)
B)
C)
D)
E)

Question 53

The cost of college tuition (in hundreds of dollars) at a local community college at time t (in decades) is modeled by . What is the cost of tuition after one year?

A) $7590
B) $591.19
C) $575
D) $9234.37
E) $759

Question 54

The amount of caffeine (in milligrams) left in an adult body t hours after drinking a 16 oz. coke is modeled by . What is the one-minute decay factor (rounded to the nearest thousandth?

A) 0.016
B) 0.999
C) 0.930
D) 0.957
E) 1.011

Question 55

Morphine is administered to a patient intravenously with an initial amount of 13 mg. About 32.8% of the morphine in a patient's body is metabolized and leaves the body each hour. What is the 4-hour decay factor for the amount of morphine remaining in the body (rounded to the nearest thousandth)?

A) 2.651
B) 0.012
C) 8.736
D) 0.204
E) 0.150

Question 56

Atmospheric pressure (measured in atm) decreases by 11.5% for every 1000-meter increase in elevation. At sea level the atmospheric pressure is 1 atm. What is the atmospheric pressure at 8000 meters above sea level (rounded to the nearest thousandth)?

A) 0.376
B) 0.115
C) 0.985
D) 0.885
E) 0.998

Question 57

Morphine is administered to a patient intravenously with an initial amount of 15 mg. About 33.1% of the morphine in a patient's body is metabolized and leaves the body each hour. How much morphine will be left after 2.6 hours (rounded to the nearest hundredth)?

A) 0.35
B) 0.85
C) 5.27
D) 0.67
E) 10.04

Question 58

A certain region started with 187 wild coyotes. Due to drought the region had only 46 coyotes remaining after 6 months. Which of the following is the 6-month decay factor (rounded to the nearest hundredth)?

A) 5.20
B) 47.00
C) 0.63
D) 0.25
E) 4.07

Question 59

Morphine is administered to a patient intravenously with an initial amount of 11 mg. About 36.9% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body after t hours?

A)
B)
C)
D)
E)

Question 60

Morphine is administered to a patient intravenously with an initial amount of 14 mg. About 26.7% of the morphine in a patient's body is metabolized and leaves the body each hour. Which one of the following models the amount of morphine remaining in the body for 1.5-hour periods of time?

A)
B)
C)
D)
E)

Question 61

Marcus wishes to invest $2500 in a 3-year CD that has an interest rate of 4.5% each year compounded twice a year. What will the CD be worth after 3 years (rounded to the nearest hundredth)?

A) $2946050.42
B) $2672.58
C) $2612.50
D) $2857.06
E) $2730.06

Question 62

The graph of a function that models exponential decay is shown. What is the initial population?

A) Not enough information
B) 10
C) 0
D) 1300
E) 910

Question 63

Sally wishes to invest $4500 in a 2-year CD with an interest rate of 5.3% each year and compounded monthly. What is the annual percentage yield for Sally's CD (rounded to the nearest hundredth)?

A) 5.43%
B) 1.05%
C) 5.3%
D) 11.16%
E) 0.44%

Question 64

Using the following table of a function that models exponential decay determine the one-year decay factor (rounded to the nearest thousandth).

A) 0.210
B) 0.790
C) 0.624
D) 0.376
E) Not enough information

Question 65

Using the following table of a function that models exponential decay determine which one of the following models the amount of radioactive substance as a function of time?

A)
B)
C)
D)
E)

Question 66

Justin wishes to invest $7000 in a 3-year CD with an interest rate of 6.2% each year and compounded daily. What is the annual percentage yield for Justin's CD (rounded to the nearest hundredth)?

A) 6.40%
B) 6.20%
C) 20.44%
D) 1.06%
E) 0.02%

Question 67

Using the following table of a function that models exponential decay determine the initial value (rounded to the nearest integer).

A) 36.78
B) 5086.88
C) 1483.33
D) 801.00
E) 17444.71

Question 68

Using the following table of a function that models exponential decay determine the one-year decay factor (rounded to the nearest hundredth).

A) 0.02
B) 0.44
C) 0.56
D) 0.22
E) 0.81

Question 69

Using the following table of a function that models exponential growth determine the one-year growth factor (rounded to the nearest hundredth).

A) 1.32
B) 1.75
C) 0.87
D) 1.15
E) 0.76

Question 70

Sara invested $5700 into an account with an interest rate of 3.3% each year compounded daily. How much money will be in the account after 3 years (rounded to the nearest hundredth)?

A) $5891.23
B) $6293.15
C) $6283.13
D) $798899612.18
E) $5888.10

Question 71

Zachary invested $4000 into an account with an interest rate of 5.3% each year compounded monthly. How much money will be in the account after 1 month (rounded to the nearest hundredth)?

A) $322432.10
B) $4217.23
C) $4212.00
D) $4017.67
E) $4435.24

Question 72

Using the following table of a function that models exponential decay determine the initial value (rounded to the nearest integer).

A) 880
B) 668
C) 508
D) 293
E) Not enough information

Question 73

Jessica invested $10700 into an account with an interest rate of 4.7% per year compounded quarterly. How much money will be in the account after 1 month (rounded to the nearest hundredth)?

A) $11202.90
B) $10825.73
C) $12857.91
D) $11211.83
E) $239453.30

Question 74

The graph of a function that models exponential growth is shown. What is the one-year growth factor?

A) 1.8
B) 5.8
C) 400
D) 0.8
E) 0

Question 75

The graph of a function that models exponential decay is shown. What is the one-year decay factor?

A) 1.3
B) 0.2
C) 0.8
D) 1440
E) 0.6

Question 76

Using the following table of a function that models exponential decay determine the one-month decay factor (rounded to the nearest thousandth).

A) 0.830
B) 0.069
C) 0.689
D) 0.170
E) 0.985

Question 77

Using the following table of a function that models exponential growth determine the initial value of the population (rounded to the nearest integer).

A) 1559
B) 1700
C) 1836
D) 1457
E) 1417

Question 78

The graph of a function that models exponential growth is shown. What is the initial population?

A) 0
B) 300
C) Not enough information
D) 390
E) 1.3

Question 79

Using the following table of a function that models exponential growth determine which one of the following models the population as a function of time.

A)
B)
C)
D)
E)

Question 80

Using the following table of a function that models exponential growth determine the one-year growth factor (rounded to the nearest thousandth).

A) Not enough information
B) 1.080
C) 0.857
D) 1.166
E) 0.926