Question

the squirrel population in a small self-contained forest was studied by a biologist. the biologist found that the squirrel population, P, measured in hundreds, is a function of time, t, where t is measured in weeks. the function P(t)=20/(1+3e^0.02t). the biologists study the squirrel population for 52 weeks.
a) determine the maximum population of squirrels over the first 52 weeks. (remember to check the endpoints and the critical point)
b) as time goes to infinity what will the limit of P(t) be? (you should be able to do this without a calculator)
c) how does what you discovered in b) confirm what you learned in a?
e) determine the point of inflection.
f) explain the meaning of the point of inflect in terms of the squirrel population growth.

Answer 1

P(t)=20/(1+3e^0.02t)
= 20(1+3e^0.02t)^-1
P ' (t) = -20(1+3e^0.02t)^-2 (.06)(e^(.02t) )(.02)
= -.024(e^(.02t) ) / (1+3e^0.02t)^2

check my steps, I should have written it out on paper