Question 1

Solve.
-Using the chessboard parable, find the total number of grains when all squares up to and including 13 are filled.

Accepted Answer

A) 2048 grains 
B) 24 grains 
C) 4096 grains 
D) 8191 grains

Question 2

Use the decibel scale to answer the question.
-What is the loudness, in decibels, of a sound 67 million times as loud as the softest audible sound?

Accepted Answer

A) 63 dB 
B) 94 dB 
C) 110 dB 
D) 78 dB

Question 3

Provide an appropriate response.
-Given $\log _ { 10 } 2 = 0.3010$ and $\log _ { 10 } 3 = 0.4771$, find $\log _ { 10 } 54$ without using a calculator.

Accepted Answer

A)  $0.4308$ 
B)  $1.3801$ 
C)  $1.7323$ 
D)  $0.4096$

Question 4

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.

Accepted Answer

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

Question 5

Provide an appropriate response.
-A community of rats begins with an initial population of 100 and grows 4% per month. Find the doubling time of the population. Round to the nearest month.

Accepted Answer

A) 23 months 
B) 28 months 
C) 14 months 
D) 18 months

Question 6

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

Accepted Answer

A)  $7.9 \times 10 ^ { 13 }$ joules 
B)  $7.9 \times 10 ^ { 11 }$ joules 
C)  $2.5 \times 10 ^ { 9 }$ joules 
D)  $7.6 \times 10 ^ { 11 }$ joules

Question 7

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?

Accepted Answer

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

Question 8

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).

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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 1850 and 1950 , which was about $0.4 \%$.

Accepted Answer

A)  177 years; population in 50 years $= 126,827$ 
B)  170 years; population in 50 years $= 112,617$ 
C)  185 years; population in 50 years $= 117,167$ 
D)  175 years; population in 50 years $= 121,901$

Question 11

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

Accepted Answer

A)  $2 ^ { 57 }$ bacteria 
B)  $2 ^ { 56 }$ bacteria 
C)  59 bacteria 
D)  114 bacteria

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?

Accepted Answer

A)  $2^{1 / 12}$ 
B)  $2 ^ { 36 }$ 
C)  $2 ^ { 12 }$ 
D)  36

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

Provide an appropriate response.
- $\log _ { 10 } \frac { 1 } { 11 }$is between 0 and 1.

Accepted Answer

A) True 
 B)False

Question 16

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?

Accepted Answer

A)  Exponential; $\$ 8614.22$ 
B)  Linear; $\$ 10,918.88$ 
C)  Linear; \$12,088.76 
D)  Exponential; $\$ 7549.63$

Question 17

Determine whether the growth (or decay)is linear or exponential, and answer the associated question.
-The population of Oak Forest is increasing at a rate of 4% per year. If the population is 39,410 today, what will it be in three years?

Accepted Answer

A) Linear; 64,410 people 
B) Exponential; 44,331 people 
C) Exponential; 41,008 people 
D) Linear; 122,959 people

Question 18

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

Accepted Answer

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 19

Provide an appropriate response.
-Urban encroachment is causing the area of a forest to decline at a rate of 5% per year. Use the approximate half-life formula to determine the half-life of the forest.

Accepted Answer

A) 12.00 years 
B) 14.00 years 
C) 28.00 years 
D) 1.05 years

Question 20

Provide an appropriate response.
-The loudness of a sound in decibels is defined by the formula $$10 \log _ { 10 } \left( \frac { \text { intensity of the sound } } { \text { intensity of loudest audible sound } } \right)$$

Accepted Answer

A) True 
 B)False

Exam 8: Exponential Astonishment

Solve. -Using the chessboard parable, find the total number of grains when all squares up to and including 13 are filled.

Use the decibel scale to answer the question. -What is the loudness, in decibels, of a sound 67 million times as loud as the softest audible sound?

Provide an appropriate response. -Given $\log _ { 10 } 2 = 0.3010$ and $\log _ { 10 } 3 = 0.4771$ , find $\log _ { 10 } 54$ without using a calculator.

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.

Provide an appropriate response. -A community of rats begins with an initial population of 100 and grows 4% per month. Find the doubling time of the population. Round to the nearest month.

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

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?

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) .

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

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 1850 and 1950 , which was about $0.4 \%$ .

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

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?

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

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

Provide an appropriate response. - $\log _ { 10 } \frac { 1 } { 11 }$ is between 0 and 1.

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?

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. -The population of Oak Forest is increasing at a rate of 4% per year. If the population is 39,410 today, what will it be in three years?

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

Provide an appropriate response. -Urban encroachment is causing the area of a forest to decline at a rate of 5% per year. Use the approximate half-life formula to determine the half-life of the forest.

Provide an appropriate response. -The loudness of a sound in decibels is defined by the formula $10 \log _ { 10 } \left( \frac { \text { intensity of the sound } } { \text { intensity of loudest audible sound } } \right)$

Exam 8: Exponential Astonishment

Solve. -Using the chessboard parable, find the total number of grains when all squares up to and including 13 are filled.

Use the decibel scale to answer the question. -What is the loudness, in decibels, of a sound 67 million times as loud as the softest audible sound?

Provide an appropriate response. -Given log⁡102=0.3010\log _ { 10 } 2 = 0.3010log10​2=0.3010 and log⁡103=0.4771\log _ { 10 } 3 = 0.4771log10​3=0.4771 , find log⁡1054\log _ { 10 } 54log10​54 without using a calculator.

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.

Provide an appropriate response. -A community of rats begins with an initial population of 100 and grows 4% per month. Find the doubling time of the population. Round to the nearest month.

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

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?

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) .

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

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 1850 and 1950 , which was about 0.4%0.4 \%0.4% .

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

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?

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

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

Provide an appropriate response. - log⁡10111\log _ { 10 } \frac { 1 } { 11 }log10​111​ is between 0 and 1.

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?

Determine whether the growth (or decay) is linear or exponential, and answer the associated question. -The population of Oak Forest is increasing at a rate of 4% per year. If the population is 39,410 today, what will it be in three years?

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

Provide an appropriate response. -Urban encroachment is causing the area of a forest to decline at a rate of 5% per year. Use the approximate half-life formula to determine the half-life of the forest.

Provide an appropriate response. -Given $\log _ { 10 } 2 = 0.3010$ and $\log _ { 10 } 3 = 0.4771$ , find $\log _ { 10 } 54$ without using a calculator.

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 1850 and 1950 , which was about $0.4 \%$ .

Provide an appropriate response. - $\log _ { 10 } \frac { 1 } { 11 }$ is between 0 and 1.