Deck 8: Exponential Astonishment

Question 1

Solve.
Using the chessboard parable, find the total weight (in pounds )when all squares up to and including 15 are filled. Assume that each grain of wheat weighs 1/7000 pound. Round your answer
To the nearest pound.

A)4 pounds
B)1 pounds
C)2 pounds
D)5 pounds

Answer 1

D

Question 2

Provide an appropriate response.
A community of deer begins with an initial population of 1000 and grows 0.8% per year. Find the doubling time of the population. Round to the nearest year.

A)1 year
B)87 years
C)250 years
D)38 years

Answer 2

B

Question 3

Use the earthquake magnitude scale to answer the question.
Compare the energy of a magnitude 6 earthquake to that released by a 1-megaton nuclear bomb

A)133.3 times as much energy
B)200.0 times as much energy
C)114.3 times as much energy
D)20.8 times as much energy

Answer 3

B

Question 4

Provide an appropriate response.
Suppose a radioactive substance has a half-life of 2000 years. What fraction will be left after 8000 years?

Question 5

Provide an appropriate response.
Urban encroachment is causing the area of a forest to decline at a rate of 6% per year. Use the approximate half-life formula to determine the fraction that remains in 66 years.

A)0.942318
B)2.828571
C)0.019817
D)0.520202

Question 6

Provide an appropriate response.
True or False? Money in a bank account earning compound interest at an annual percentage rate of
3% represents an example of linear growth.

Question 7

Provide an appropriate response.
Earthquakes usually cause damage in all but which one of the following related ways?

A)Collapsed building due to inferior construction
B)Landslides
C)Fires caused by heat from the earth's interior.
D)Tsunamis

Question 8

Use the decibel scale to answer the question.
How much louder (more intense)is a 60-dB sound than a 50-dB sound?

A)1.2 times as loud
B)10,000,000 times as loud
C)25 times as loud
D)10 times as loud

Question 9

Provide an appropriate response.
True or False? Bases have a pH Lower than 7.

Question 10

Provide an appropriate response.
True or False? Our town is growing with a doubling time of 40 years, so its population will triple
in 120 years.

Question 11

Provide an appropriate response.
Which of the following sounds would you expect to have the highest decibel measurement?

A)Ordinary conversation
B)Background noise in an average home
C)Rustling leaves
D)Afternoon traffic in New York City

Question 12

Provide an appropriate response.
The doubling time of a population of flies is 3 hours. By what factor does the population increase in 36 hours?

Question 13

Provide an appropriate response.
Use the growth rate of 1.3% to estimate the population of a growing country in 2097. Start from the 2000 population of 62 million. Use the approximate doubling time formula.

A)216.1 million
B)143.7 million
C)162.0 million
D)91.1 million

Question 14

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
The value of your house is rising by 19% per year. If it is worth $319,738 today, what will it be worth in three years?

A)Exponential; $384,416.96
B)Linear; $441,238.44
C)Exponential; $538,809.37
D)Linear; $501,988.66

Question 15

Provide an appropriate response.
Consider a population that begins growing exponentially at a base rate of 8% per year and then follows a logistic growth pattern. If the carrying capacity is 90 million, find the actual growth rate
When the population is 76 million.

A)1.24%
B)1.41%
C)1.12%
D)1.33%

Question 16

Provide an appropriate response.
Which of the following are factors in the amount of damage caused by an earthquake?

A)The type of surface bedrock near the quake
B)All of these
C)The amount of energy released in surface waves as compared to interior waves
D)The economy of the region hit by the earthquake

Question 17

Use the earthquake magnitude scale to answer the question.
How many times as much energy is released by an earthquake of magnitude 8 as by one of magnitude 2?

Question 18

Use the pH scale to answer the question.
If the pH of a solution increases by 3, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?

A)Decreases by a factor of 30; more basic
B)Increases by a factor of 1000; more acidic
C)Increases by a factor of 30; more acidic
D)Decreases by a factor of 1000; more basic

Question 19

Provide an appropriate response.
True or False? Birth rates have increased rapidly throughout the world during the past 50 years.

Question 20

Provide an appropriate response.
True or False? The carrying capacity is the largest population the environment can support for extended periods of time.

A)False
B)True

Question 21

Provide an appropriate response.
Suppose a population has a doubling time of 40 years. By what factor will it grow in 40 years?

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

Question 22

Use the pH scale to answer the question.
What is the hydrogen ion concentration of a solution with pH 2.5?

Question 23

Provide an appropriate response.
Use the growth rate of 0.7% to estimate the population of a growing country in 2072. Start from the 2000 population of 50 million. Use the approximate doubling time formula.

A)93.3 million
B)82.4 million
C)102.0 million
D)130.9 million

Question 24

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
The population of Scoville is increasing at a rate of 405 people per year. If the population is 696 today, what will it be in three years?

A)Exponential; 337,153,941 people
B)Linear; 1911 people
C)Linear; 2493 people
D)Exponential; 66,430,821 people

Question 25

Solve.
Use the magic penny parable to determine how much money you would have after 8 days.

A)$5.12
B)$1.28
C)$655.36
D)$2.56

Question 26

Provide an appropriate response.
The Consumer Price Index is increasing at a rate of 8% per year. What is its doubling time? Use the approximate doubling time formula (rule of 70).

A)8.75 years
B)256 years
C)5.6 years
D)16 years

Question 27

Provide an appropriate response.
True or False? Repeated doubling, in which each doubling occurs in the same amount of time, is a hallmark of linear growth.

A)False
B)True

Question 28

Provide an appropriate response.
True or False? is between 0 and 1.

Question 29

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
The value of your car is decreasing by 12% per year. If the car is worth $9749 today, what will it be worth in two years?

Question 30

Solve.
Use the magic penny parable to determine how many days would elapse before you had a total of over $6,029,920.

A)21 days
B)33 days
C)38 days
D)29 days

Question 31

Provide an appropriate response.
True or False? is between 0 and 1.

A)False
B)True

Question 32

Provide an appropriate response.
True or False? Earthquake strength is described in decibels, the loudness of sounds is described in
pH, and the acidity of household cleansers is described by magnitudes.

Question 33

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
The price of computer memory is decreasing at a rate of 14% per year. If a memory chip costs $90 today, what will it cost in two years?

A)Linear; $64.80
B)Exponential; $66.56
C)Linear; $115.20
D)Exponential; $77.84

Question 34

Use the earthquake magnitude scale to answer the question.
How much energy, in joules, is released by an earthquake of magnitude 5?

Question 35

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growingsuburban town (based on a current population of 100,000).
Use the average growth rate between 1970 and 2000, which was about 0.7%.

A)95 years; population in 50 years = 123,114
B)100 years; population in 50 years = 141,421
C)102 years; population in 50 years = 151,572
D)110 years; population in 50 years = 131,951

Question 36

Provide an appropriate response.
_______ growth occurs when a quantity grows by the same relative amount in each unit of time.

A)Linear
B)Exponential
C)Static
D)None of the above

Question 37

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growingsuburban town (based on a current population of 100,000).

Question 38

Provide an appropriate response.
True or False? is between 10 and 100.

A)False
B)True

Question 39

Provide an appropriate response.

Question 40

Provide an appropriate response.
Inflation is causing prices to rise at a rate of 9% per year. Use the approximate double time formula to determine what the price will be in 11 years if the item costs $100 today.

A)$533.06
B)$313.83
C)$266.53
D)$109.32

Question 41

Provide an appropriate response.
True or False? log101,400,000 is between 6 and 7.

A)False
B)True

Question 42

Use the earthquake magnitude scale to answer the question.
How much energy, in joules, is released by an earthquake of magnitude 5.8?

Question 43

Provide an appropriate response.
The initial population of a town is 16,237 and it grows with a doubling time of 24 years. What will the population be in 2 years?

A)17,203 people
B)32,474 people
C)16,238 people
D)64,948 people

Question 44

Provide an appropriate response.
If a population has exceeded the carrying capacity of its environment, it may suffer a rapid and severe decrease in the population. What is the name of this type of population decrease?

A)Overshoot
B)Logistic growth
C)Annual growth rate
D)Collapse

Question 45

Solve.
Use the bacteria parable to determine how many bacteria are in the bottle at 11:57.

Question 46

Use the decibel scale to answer the question.
How does the intensity of sound from a concert speaker at a distance of 10 meters compare to the intensity at a distance of 40 meters?

A)Factor of 40 weaker at 40 m.
B)Factor of 4 weaker at 40 m.
C)Factor of 64 weaker at 40 m.
D)Factor of 16 weaker at 40 m.

Question 47

Provide an appropriate response.
True or False? Exponential growth leads to repeated doublings. With each doubling, the amount
of increase is approximately equal to the sum of all preceding doublings.

Question 48

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
The price of a gallon of gasoline is increasing by 1¢ per week. If the price is $3.08 per gallon today, what will it be in ten weeks?

A)Exponential; $3.40
B)Linear; $3.18
C)Linear; $3.17
D)Exponential; $3.11

Question 49

Provide an appropriate response.
The Consumer Price Index is increasing at a rate of 5% per year. By what factor will prices increase in 2 years? Use the approximate doubling time formula (rule of 70).

A)5.1
B)20
C)1
D)1.1

Question 50

Provide an appropriate response.
True or False? Pure water is neutral and has a pH of 0.

Question 51

Provide an appropriate response.
True or False? The world population growth rate is equal to the birth rate subtracted from the death rate.

A)False
B)True

Question 52

Solve.
Use the bacteria parable to determine what fraction of the bottle is full at 11:39.

Question 53

Provide an appropriate response.
In 2000, the population of Littletown was 8 thousand. Use the given doubling time to predict the population in 2010. Assume a doubling time of 30 years.

A)10.1 thousand
B)2400 thousand
C)12.7 thousand
D)1.3 thousand

Question 54

Provide an appropriate response.

Question 55

Provide an appropriate response.
Real populations sometimes increase beyond their environment's carrying capacity in a relatively short period of time. What is the name of this phenomenon?

A)Annual growth rate
B)Logistic growth
C)Overshoot
D)Collapse

Question 56

Provide an appropriate response.
True or False? When the population is small relative to the carrying capacity, logistic growth is
exponential with a fractional growth rate close to the base growth rate r.

Question 57

Provide an appropriate response.
Consider a population that begins growing exponentially at a base rate of 2% per year and then follows a logistic growth pattern. If the carrying capacity is 41 million, find the actual growth rate
When the population is 14 million.

A)1.19%
B)1.49%
C)1.41%
D)1.32%

Question 58

Provide an appropriate response.
True or False? The earthquake magnitude scale relates the magnitude to the amount of energy released.

A)False
B)True

Question 59

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
The value of your house is rising by $24,731 per year. If it is worth $199,401 today, what will it be worth in three years?

A)Exponential; $283,176.32
B)Linear; $273,594.00
C)Linear; $622,934.00
D)Exponential; $672,396.00

Question 60

Provide an appropriate response.
True or False? An earthquake of magnitude 2 will do twice as much damage as an earthquake of magnitude 1.

A)False
B)True

Question 61

Provide an appropriate response.
In 2000, the population of Littletown was 16 thousand. Use the given doubling time to predict the population in 2060. Assume a doubling time of 30 years.

A)28,800 thousand
B)32.0 thousand
C)4.0 thousand
D)64.0 thousand

Question 62

Provide an appropriate response.

Question 63

Use the decibel scale to answer the question.
How does the intensity of sound form a concert speaker at a distance of 1 meter compare to the intensity at a distance of 800 meters?

A)Factor of 10800 weaker at 800 m.
B)Factor of 640,000 weaker at 800 m.
C)Factor of 2400 weaker at 800 m.
D)Factor of 800 weaker at 800 m.

Question 64

Provide an appropriate response.
The current population of a threatened animal species is 1 million, but it is declining with a half-life of 27 years. How many animals will be left in 74 years?

A)149,608 animals
B)150 animals
C)74,804 animals
D)748 animals

Question 65

Solve.
Use the magic penny parable to determine how many days would elapse before you had a total of over 155,235.

A)33 days
B)24 days
C)28 days
D)16 days

Question 66

Provide an appropriate response.
What are the conditions in which the approximate doubling time formula works well?

A)small growth rates and breaks down for growth rates over 15%
B)large growth rates and breaks down for growth rates below 30%
C)large growth rates and breaks down for growth rates below 15%
D)small growth rates and breaks down for growth rates over 30%

Question 67

Use the decibel scale to answer the question.
How does the intensity of sound from a concert speaker at a distance of 20 meters compare to the intensity at a distance of 140 meters?

A)Factor of 7 weaker at 140 m.
B)Factor of 49 weaker at 140 m.
C)Factor of 196 weaker at 140 m.
D)Factor of 70 weaker at 140 m.

Question 68

Provide an appropriate response.
Use the 1960s peak annual growth rate of 2.5% and population of 4 million to predict the current growth rate with a logistic model. Assume a current country population of 10 million. Assume the
Carrying capacity is 21 million.

A)4.71%
B)2.50%
C)2.43%
D)1.62%

Question 69

Provide an appropriate response.
Poaching is causing a population of elephants to decline by 6% per year. Use the approximate half-life formula to determine the fraction that remains in 76 years if there are 13,365 elephants
Today.

A)146 elephants
B)6297 elephants
C)43,532 elephants
D)12,594 elephants

Question 70

Provide an appropriate response.
Inflation is causing prices to rise at a rate of 6% per year. Use the exact double time formula to determine what the price will be in 4 years if the item costs $100 today.

A)$100.24
B)$126.25
C)$100.28
D)$100.06

Question 71

Provide an appropriate response.
The half-life of a radioactive substance is 65 years. If you start with some amount of this substance, what fraction will remain in 132 years?

A)0.24
B)0.06
C)0.01
D)4.09

Question 72

Provide an appropriate response.
The initial population of a town is 128,066 and it grows with a doubling time of 97 years. What will the population be in 35 years?

A)128,090 people
B)8,964,620 people
C)4,482,310 people
D)164,457 people

Question 73

Provide an appropriate response.
The number of cells in a tumor doubles every 3.7 months. If the tumor begins as a single cell, how many cells will there be after 3 years?

A)849 cells
B)123 cells
C)2 cells
D)133 cells

Question 74

Provide an appropriate response.
A certain radioactive isotope decays at a rate of 0.15% per year. Determine the half-life of this isotope, to the nearest year.

A)462 years
B)201 years
C)5 years
D)333 years

Question 75

Use the decibel scale to answer the question.
What is the loudness, in decibels, of a sound 16 trillion times as loud as the softest audible sound?

A)106 dB
B)158 dB
C)185 dB
D)132 dB

Question 76

Provide an appropriate response.
Use the 1960s peak annual growth rate of 0.4% and population of 6 million to predict the current growth rate with a logistic model. Assume a current country population of 15 million. Assume the
Carrying capacity is 26 million.

A)0.33%
B)0.22%
C)0.74%
D)0.40%

Question 77

Provide an appropriate response.
Oil consumption is increasing at a rate of 2.1% per year. By what factor will oil consumption increase in 2 years? Use the approximate doubling time formula (rule of 70).

A)2.14
B)1.04
C)8.4
D)1.01

Question 78

Use the given growth rate to find the approximate doubling time and to predict the population in 50 years of a growingsuburban town (based on a current population of 100,000).
Use the current annual growth rate which is about 3.1%.

Question 79

Provide an appropriate response.
True or False? The carrying capacity of our planet depends on our consumption of energy.

A)False
B)True

Question 80

Use the pH scale to answer the question.
What is the pH of a solution with a hydrogen ion concentration of 0.001 mole per liter? Is this solution an acid or a base?