Chapter 8 Review
8A
Name:______________________
1. The price of a certain product is increasing at a rate of $2.30 per year. Explain whether this statement
describes a linear or exponential relationship.
2. The value of farm land in a certain state is increasing at a rate of 4% per year. Explain whether this
statement describes a linear or exponential relationship.
3. The Board of Directors of a neighborhood Home Owner’s Association has decided they need to raise
dues by 10% each and every year to help pay for pool improvements. If dues are $60 per month this
year, how much will they be in 6 years?
4. Suppose a chess board has one grain of wheat on the first square, two grains on the second square, four
grains on the third square, eight grains on the fourth square, and so on, up to and including the 18th
square. Find the total number of grains on the board.
5. Suppose a leprechaun gives you a magic penny (on day 0) that doubles every night. How much money
would you have after 20 days?
6. Suppose that a single bacterium is in a bottle at 11:00 am. It divides into two bacteria at 11:01, and the
population continues to double every minute until the bottle is completely full at 12:00 noon. Find the
population of bacteria at 11:25 am.
7. Suppose that a single bacterium is in a bottle at 11:00 am. It divides into two bacteria at 11:01, and the
population continues to double every minute until the bottle is completely full at 12:00 noon. Find the
fraction of the bottle that is full at 11:51 am.
8. Suppose that a single bacterium exists at 11:00 am. It divides into two bacteria at 11:01, and the
population continues to double every minute. If each bacterium has a volume of 10−21 𝑚3 , how deep
would the bacteria be at 1:08 pm if they were spread in a uniform layer all over the surface of the Earth?
(Assume that the surface area of the Earth is 5.1 x 1014 m², and show your work.)
9. The population of a certain city is now 74,000 people. If the population doubles every 25 years, what
will the population be after 125 years?
8B
1. If a quantity quadruples every 16 days, what is its doubling time?
2. Suppose that a population has a doubling time of 18 years. By what factor will it grow in 72 years?
3. Suppose that you possess some of a radioactive substance that has a half-life of 31 days. What fraction
of the substance will remain after 217 days?
4. If the doubling time of a state’s population is 38 years, how long does it take for the population to
increase by a factor of 8?
5. Suppose you deposit $2500 in a bank account that has a doubling time of 14 years. What will your
balance be after 45 years?
6. Since 1913, inflation has caused prices to double about every 21.3 years. By what factor do prices
increase each year?
7. Suppose you are using the approximate half-life formula to determine the half-lives corresponding to
several different decay rates. Will you obtain exact results? If not, explain when your results will be the
least accurate.
8. Suppose that the consumer price index of a country is decreasing at the rate of 4.3% per year. Use the
approximate half-life formula to estimate the half-life.
9. Suppose that a quantity is halved every 20 years. Use the approximate half-life formula to estimate its
decay rate.
10. If the half-life of a drug in the bloodstream is 15 hours, how much drug is left in the bloodstream 36
hours after a 400 milligram dose?
8C
1. Explain the meaning of carrying capacity.
2. For Australia in 2009, the birth rate was approximately 1.25 births per 100 people per year and the death
rate was approximately .67 deaths per 100 people per year. Find the population growth rate as a
percentage. (Neglect the effects of immigration and emigration.)
3. The population growth rate of China has been estimated at .67% per year. What is the approximate
doubling time?
4. If the population of Idaho is now 1,524,000 and the population growth rate is 1.8% per year, what will
the population be in 30 years?
5. Suppose that a country’s population is 64 million and its population growth rate is 3.7% per year. If the
population growth follows a logistic growth model with r = 0.053, what is the country’s carrying
capacity?
6. The table gives the birth and death rates for Greece between 1988 and 2005.
Birth Rate (per
Death Rate (per
Growth Rate (% per
Year
1000)
1000)
year)
1988
15.4
9.1
1998
10.2
9.3
2005
10
10
a. Describe the general trend in the birth rate between 1988 and 2005.
b. Describe the general trend in the death rate between 1988 and 2005.
c. Complete the table to show the country’s net growth rate due to births and deaths in 1988, 1998, and
2005. Neglect the effects of immigration.
d. Based on your answers to parts (a) through (c), predict how the country’s population will change over
the next 20 years. Do you think your prediction is reliable? Explain.
7. Suppose the population of a country changes due to births, deaths, and immigration. The annual birth
rate is 5.6 births per 1000 people, the death rate is 4.3 deaths per 1000 people, the immigration rate into
the country is 7.8 per 1000, and the emigration rate out of the country is 2.4 per 1000. Find the net
growth rate as a percentage.
8. Suppose a country currently has a population of 18 million and an annual growth rate of 2.50%. If the
population growth follows a logistic growth model with a carrying capacity of 65 million, calculate the
annual growth rate when the population is 32 million.
Unit 8D Test 1
1. Give one reason why earthquakes of the same magnitude may cause different amounts of damage.
2. Give a possible explanation for why the 1990 earthquake in Iran of magnitude 7.7 caused so many more
deaths than the relatively comparable earthquake in 1997.
3. Compare the estimated energies released by the 1989 earthquake in San Francisco of magnitude 7.1 and
the 1994 earthquake in Los Angeles of magnitude 6.7. Show your work.
4. What is a sound of 0 decibels defined to be?
5. Suppose that a sound is 1500 times as intense as the softest audible sound. What is its loudness, in
decibels?
6. How much more intense is a 115 dB sound than a 65 dB sound?
7. The sound level from a television 1 meter away is 130 dB. How far away from the television should you
be to avoid risking damage to your ears?
8. Name something in a refrigerator that probably has a pH value lower than 7.
9. What is the pH of a solution with a hydrogen ion concentration of 10−11 moles per liter?
10. Name something that can cause acid rain.