Question 1

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

Accepted Answer

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

Question 2

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.

Accepted Answer

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

Question 3

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.

Accepted Answer

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

Question 4

Provide an appropriate response.
-In 2000, the population of Littletown was 13 thousand. Use the given doubling time to predict the population in 2100. Assume a doubling time of 40 years.

Accepted Answer

A) 5.7 thousand 
B) 73.5 thousand 
C) 416.0 thousand 
D) 52,000 thousand 
A) 5.7 thousand 
B) 73.5 thousand 
C) 416.0 thousand 
D) 52,000 thousand

Question 5

Provide an appropriate response.
-Bases have a pH Lower than 7.

Accepted Answer

A) True 
 B)False

Question 6

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?

Accepted Answer

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. 
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 7

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).

Accepted Answer

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

Question 8

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%.

Accepted Answer

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 
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 9

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?

Accepted Answer

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

Question 10

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

Accepted Answer

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 
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 11

Use the decibel scale to answer the question.
-How many times as loud as the softest audible sound is the sound of background noise in average home (40 decibels)?

Accepted Answer

A)  $10 ^ { 3 }$ 
B)  $10 ^ { 4 }$ 
C)  $10 ^ { 8 }$ 
D)  $10 ^ { 40 }$ 
A)  $10 ^ { 3 }$ 
B)  $10 ^ { 4 }$ 
C)  $10 ^ { 8 }$ 
D)  $10 ^ { 40 }$

Question 12

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.

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  16 
C)  8 
D)  $\frac { 1 } { 16 }$ 
A)  $\frac { 1 } { 8 }$ 
B)  16 
C)  8 
D)  $\frac { 1 } { 16 }$

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

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 $\left( 5 \times 10 ^ { 15 } \text { joules } \right)$

Accepted Answer

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 
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

Question 16

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?

Accepted Answer

A)  $10 ^ { 2 }$ times as much energy 
B)  $10 ^ { 4 }$ times as much energy 
C)  $10 ^ { 6 }$ times as much energy 
D)  $10 ^ { 9 }$ times as much energy 
A)  $10 ^ { 2 }$ times as much energy 
B)  $10 ^ { 4 }$ times as much energy 
C)  $10 ^ { 6 }$ times as much energy 
D)  $10 ^ { 9 }$ times as much energy

Question 17

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.

Accepted Answer

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

Question 18

Provide an appropriate response.
-Birth rates have increased rapidly throughout the world during the past 50 years.

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

A)  $1.2 \times 10 ^ { 13 }$ joules 
B)  $7.9 \times 10 ^ { 15 }$ joules 
C)  $1.6 \times 10 ^ { 10 }$ joules 
D)  $1.3 \times 10 ^ { 13 }$ joules 
A)  $1.2 \times 10 ^ { 13 }$ joules 
B)  $7.9 \times 10 ^ { 15 }$ joules 
C)  $1.6 \times 10 ^ { 10 }$ joules 
D)  $1.3 \times 10 ^ { 13 }$ joules

Question 20

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.

Accepted Answer

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

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

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.

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.

Provide an appropriate response. -In 2000, the population of Littletown was 13 thousand. Use the given doubling time to predict the population in 2100. Assume a doubling time of 40 years.

Provide an appropriate response. -Bases have a pH Lower than 7.

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?

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).

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%.

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?

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

Use the decibel scale to answer the question. -How many times as loud as the softest audible sound is the sound of background noise in average home (40 decibels)?

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.

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

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

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 $\left( 5 \times 10 ^ { 15 } \text { joules } \right)$

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?

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.

Provide an appropriate response. -Birth rates have increased rapidly throughout the world during the past 50 years.

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

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.

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Putting Statistics to Work

Probability: Living With the Odds

Modeling Our World

Modeling With Geometry

Mathematics and the Arts

Filters

Exam 8: Exponential Astonishment

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

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.

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.

Provide an appropriate response. -In 2000, the population of Littletown was 13 thousand. Use the given doubling time to predict the population in 2100. Assume a doubling time of 40 years.

Provide an appropriate response. -Bases have a pH Lower than 7.

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?

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).

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%.

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?

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

Use the decibel scale to answer the question. -How many times as loud as the softest audible sound is the sound of background noise in average home (40 decibels)?

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.

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

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

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 (5×1015 joules )\left( 5 \times 10 ^ { 15 } \text { joules } \right)(5×1015 joules )

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?

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.

Provide an appropriate response. -Birth rates have increased rapidly throughout the world during the past 50 years.

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

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.

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Putting Statistics to Work

Probability: Living With the Odds

Modeling Our World

Modeling With Geometry

Mathematics and the Arts

Filters

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 $\left( 5 \times 10 ^ { 15 } \text { joules } \right)$