Exponential Decay and Growth Questions

Question

In a study of an insect population, there were about 160 insects four weeks after the study began and about 342 insects after two more weeks. Assuming an exponential model, how many insects in the initial population?

In a study of an insect population, there were about 114 insects four weeks after the study began and about 332 insects after two more weeks. How many insects would there be 8 weeks into the study?

For Question 9, what would be the exponential model for the insects?

Answer 1

A = Pe^rt where A = population amount at time t, t = number of weeks, P = Population initially at t=0

r = weekly rate of change, e = an irrational constant

160 =Pe^4r in 4 weeks

342 = Pe^6r in 2 weeks later

342/160 = e^2r

2r = ln(342/160) = ln171/80

r = (ln(171/80))/2, use a calculator with a natural log function to simplify

P = 160/e^4r = 160/e^.5ln(171/80) = the initial Population

= the Population at time t=0