Question 1

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 2.6%.

Accepted Answer

A)  27 years; population in 50 years $= 362,289$ 
B)  37 years; population in 50 years $= 280,056$ 
C)  29 years; population in 50 years $= 468,670$ 
D)  22 years; population in 50 years $= 216,488$

Question 2

Use the pH scale to answer the question.
-If the pH of a solution decreases by 1.6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?

Accepted Answer

A) Decreases by a factor of 16; more basic 
B) Increases by a factor of 16; more acidic 
C) Decreases by a factor of 40; more basic 
D) Increases by a factor of 40; more acidic

Question 3

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?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

Provide an appropriate response.
-Given that $\log _ { 10 } 2 = 0.301$, find $\log _ { 10 } 16$ without using a calculator.

Accepted Answer

A)  48 
B)  8 
C)  $1.204$ 
D)  $0.027$

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

Provide an appropriate response.
-Exponential growth cannot continue indefinitely. After only a relatively large number of doublings, exponentially growing quantities reach possible proportions.

Accepted Answer

A) True 
 B)False

Question 10

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.

Accepted Answer

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

Question 11

Provide an appropriate response.
- $10 ^ { - 0.874 }$ is between 0 and 1.

Accepted Answer

A) True 
 B)False

Question 12

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?

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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.

Accepted Answer

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

Question 16

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?

Accepted Answer

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

Question 17

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.

Accepted Answer

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

Question 18

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

Accepted Answer

A)  $3.2 \times 10 ^ { - 3 }$ 
B)  $3.2 \times 10 ^ { - 4 }$ 
C)  $3.2 \times 10 ^ { - 2 }$ 
D)  $3.2 \times 10 ^ { - 5 }$

Question 19

Provide an appropriate response.
-If you decrease the amount of water in the cup, you'll decrease the pH of the water
in the cup.

Accepted Answer

A) True 
 B)False

Question 20

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.

Accepted Answer

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

Exam 8: Exponential Astonishment

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 2.6%.

Use the pH scale to answer the question. -If the pH of a solution decreases by 1.6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?

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?

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

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

Provide an appropriate response. -Given that $\log _ { 10 } 2 = 0.301$ , find $\log _ { 10 } 16$ without using a calculator.

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

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

Provide an appropriate response. -Exponential growth cannot continue indefinitely. After only a relatively large number of doublings, exponentially growing quantities reach possible proportions.

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.

Provide an appropriate response. - $10 ^ { - 0.874 }$ is between 0 and 1.

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?

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?

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

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.

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?

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.

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

Provide an appropriate response. -If you decrease the amount of water in the cup, you'll decrease the pH of the water in the cup.

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.

Exam 8: Exponential Astonishment

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 2.6%.

Use the pH scale to answer the question. -If the pH of a solution decreases by 1.6, how much does the hydrogen ion concentration change? Does the change make the solution more acidic or more basic?

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?

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

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

Provide an appropriate response. -Given that log⁡102=0.301\log _ { 10 } 2 = 0.301log10​2=0.301 , find log⁡1016\log _ { 10 } 16log10​16 without using a calculator.

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

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

Provide an appropriate response. -Exponential growth cannot continue indefinitely. After only a relatively large number of doublings, exponentially growing quantities reach possible proportions.

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.

Provide an appropriate response. - 10−0.87410 ^ { - 0.874 }10−0.874 is between 0 and 1.

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?

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?

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

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.

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?

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.

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

Provide an appropriate response. -If you decrease the amount of water in the cup, you'll decrease the pH of the water in the cup.

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.

Provide an appropriate response. -Given that $\log _ { 10 } 2 = 0.301$ , find $\log _ { 10 } 16$ without using a calculator.

Provide an appropriate response. - $10 ^ { - 0.874 }$ is between 0 and 1.