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

Accepted Answer

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

Accepted Answer

The doubling time can be found using the rule of 70, which is an approximation method stating that the doubling time (in years) is equal to 70 divided by the growth rate (in percent). For a growth rate of 0.8%, the doubling time is 70 / 0.8 = 87.5 years, rounded to the nearest year gives 87 years.

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

Accepted Answer

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

Accepted Answer

The half-life of a substance is the time it takes for half of it to decay. After 8000 years, which is four half-lives (8000/2000), the fraction remaining is $(\frac{1}{2})^4 = \frac{1}{16}$.

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

Accepted Answer

The approximate half-life formula for a quantity decreasing at a rate of $r$ per year is given by $T_{1/2} = \frac{0.693}{r}$. For a 6% decline rate, $r = 0.06$, so $T_{1/2} = \frac{0.693}{0.06} \approx 11.55$ years. To find the fraction remaining after 66 years, we use the formula for exponential decay: $N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$, where $t = 66$ years. Substituting the values, we get $N = 1 \left(\frac{1}{2}\right)^{\frac{66}{11.55}} \approx 0.019817$, indicating that about 1.9817% of the forest remains after 66 years.

Question 6

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

Compound interest results in exponential growth, not linear growth, because the interest earned each period is added to the principal, which increases the base amount that future interest is calculated on.

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

Accepted Answer

Earthquakes can indeed cause fires, but these are typically due to ruptured gas lines or electrical faults, not directly from heat from the earth's interior.

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

Accepted Answer

The decibel scale is logarithmic, meaning each 10 dB increase represents a tenfold increase in intensity. Therefore, a 60-dB sound is 10 times more intense than a 50-dB sound.

Question 9

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

Accepted Answer

Bases have a pH higher than 7, indicating they are alkaline.

Question 10

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

Accepted Answer

The doubling time of 40 years means the population will double every 40 years. In 120 years, it would have doubled three times (at 40, 80, and 120 years), resulting in a population 8 times its original size, not tripled.

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

Accepted Answer

Afternoon traffic in New York City would have the highest decibel measurement due to the high volume of vehicles, honking, and general city noise, which is significantly louder than the other options listed.

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

Accepted Answer

The population doubles every 3 hours, so in 36 hours (which is 36/3 = 12 three-hour periods), it would double 12 times. Therefore, the population increases by a factor of $2^{12}$.

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

Accepted Answer

The approximate doubling time can be calculated using the rule of 70, which states that the doubling time in years is approximately 70 divided by the growth rate. For a 1.3% growth rate, the doubling time is 70 / 1.3 ≈ 53.85 years. From 2000 to 2097 is 97 years, which is close to two doubling periods (2 * 53.85 ≈ 107.7 years). Starting with a population of 62 million, after one doubling period (approximately by 2053), the population would be 124 million. By 2097, although not a full second doubling period, the population would be approaching its second doubling, suggesting a figure closer to the next doubling point than the first, making 216.1 million (A) the most reasonable estimate given the options.

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

Accepted Answer

Exponential growth occurs when the increase is proportional to the current amount, meaning it grows by a constant percentage (in this case, 19% per year). To calculate the future value of the house after 3 years, you use the formula for exponential growth: Future Value = Present Value * (1 + rate)^time. Here, it's $319,738 * (1 + 0.19)^3, which equals approximately $538,809.37.

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%

Accepted Answer

The logistic growth rate is given by the formula: actual growth rate = base rate * (1 - (population/carrying capacity)). Substituting the given values: 0.08 * (1 - (76/90)) = 0.0124 or 1.24%.

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

Accepted Answer

All the options listed are factors that can influence the amount of damage caused by an earthquake. The type of surface bedrock can affect how the seismic waves are transmitted, the distribution of energy between surface and interior waves can influence the intensity of shaking experienced, and the economy of a region can determine how well structures are built to withstand earthquakes and how effective the response and recovery efforts are.

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? 
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

Accepted Answer

The answer of Use the earthquake magnitude scale to answer...

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

Accepted Answer

The pH scale is logarithmic, with each unit change representing a tenfold change in hydrogen ion concentration. An increase of 3 in pH means the hydrogen ion concentration decreases by 10^3, or 1000 times, making the solution more basic.

Question 19

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

Accepted Answer

Globally, birth rates have been declining over the past 50 years due to factors such as increased access to contraception, higher levels of education, especially among women, and economic development.

Question 20

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

Accepted Answer

The carrying capacity refers to the maximum number of individuals of a particular species that an environment can support sustainably over time, given the food, habitat, water, and other necessities available in the environment.

Quiz 8: Exponential Astonishment

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.

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.

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

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. -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.

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. -Earthquakes usually cause damage in all but which one of the following related ways?

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

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

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

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

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?

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.

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?

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.

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

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?

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?

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

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