Download Math 1030 Assignment: Exponential and Linear Growth, Doubling Times, and Half-Lives and more Assignments Mathematics in PDF only on Docsity!
Assignment 7
Math 1030
Due Friday, October 26th
- Exponential and Linear Growth
Answer each of the following questions, and state whether it is an example of linear growth, exponential growth, or exponential de- crease.
(a) During the worst periods of hyperinflation in Brazil, the price of food increased at a rate of 30% per month. If your food bill was $120 one month during this period, what was it three months later?
(b) The price of computer memory is decreasing at a rate of 12% per year. If a memory chip costs $50 today, what will it cost in three years?
(c) The population of Meadow View is increasing at a rate of 623 people per year. If the population is 2500 today, what will it be in four years?
- Doubling Time and Half-Life
Answer each of the following questions concerning doubling times and half-lives.
(a) The doubling time of a bank account balance is 10 years. By what factor does it grow in 30 years? in 50 years?
(b) The initial population of a town is 15,600, and it grows with a doubling time of 8 years. What will the population be in 12 years? In 24 years?
(c) The half-life of a drug in the bloodstream is 4 hours. By what factor does the concentration of the drug decrease in 24 hours? In 36 hours?
(d) Radium-226 is a metal with a half-life of 1600 years. If you start with 1 kilogram of radium-226, how much will remain after 1000 years? after 10,000 years?
- Logistic Population Growth
Consider a population that begins growing exponentilly at a base rate of 4 .0% per year and then follows a logistic growth pattern. If the carrying capacity is 60 million, find the actual growth rate when the population is 10 million, 30 million, and 50 million.
