March 20 Name:
Problems 1 - 4 : Choose the best answer to each of the following questions. Explain your reasoning with one or more complete sentences.
1. (3 pts) A town’s population increases in one year from 100,000 to 110,000. If the population is growing linearly , at a steady rate, then at the end of a second year it will be b. 120,000
Absolute growth rate os 10,000 people per year.
2. (3 pts) A town’s population increases in one year from 100,000 to 110,000. If the population is growing exponentially , at a steady rate, then at the end of a second year it will be c. 121,000
Relative growth rate (10,000 / 100,000) is 10% per year.
3. (3 pts) Which of the following is an example of linear decay ?
b. The price of gasoline is falling by $0.02 per week.
It is an absolute growth in dollars per week (not a percentage).
4. (3 pts) Which of the following is not a good approximation of a doubling time?
a. Inflation running at 35% per year will cause prices to double in about 2 years.
Rule of 70 works best when P% ¡ 15%.
Problems 5 - 6: Decide whether each of the following statements make sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
5. (2 pts) Human population has been growing exponentially for a few centuries, and we can expect this trend to continue forever in the future.
False. Exponential growth cannot be sustained forever.
6. (2 pts) A toxic chemical decays with a half-life of 10 years, so half of it will be gone
10 years from now and all the rest will be gone 20 years from now.
False. Half - of - half is 25%. After 20 years, 25% of the original amount will remain.
Problems 7 - 8: State whether the growth (or decay) is linear or exponential, and answer the associated question.

7. (3 pts) The price of a gallon of gasoline is increasing by $0.03 per week. If the price is $3.10 per gallon today, what will it be in six weeks?
Linear. $3 .
10 + 6 × $0 .
03 = $3 .
28.
8. (3 pts) The value of your house is decreasing by 3% per year. If it is worth $220,000 today, what will it be worth in three years?
Exponential. $220 , 000 × (1 − 0 .
03) 3 = $200788 .
Problems 9 - 10: Each exercise uses an exponetially growing (or decaying) quantity. Answer the questions that follow.
9. (3 pts) A city’s population is growing at a rate of 2.8% per year. What is the doubling time? By what factor will the population increase in 40 years?
Rule of 70: T double
≈ = 70 / 2 .
8 = 25 years.
Factor = 2 40 / 25 = 3 .
03 .
The population nearly triples.
10. (3 pts) The half-life of a drug in the bloodstream is 15 hours. What fraction of the original drug dose remains in 24 hours? In 48 hours?
(1 / 2) 24 / 15
(1 / 2) 48 / 15
= 0 .
3298 or 32 .
98%.
= 0 .
1088 or 10 .
88%.