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## Homework Statement

Given that a population, P, after t months, can be modeled by the logistic model

dP/dt = .3 P (3.5 - P/40).

P(0) = 30

a) Solve the diff eq

b) Find the population after 2.5 months

c) Find lim P(t) as t -> infinity

## Homework Equations

P(t) = P

_{0}P

_{1}/(P

_{0}+ (P

_{1}- P

_{0})e^(-AP

_{1}t))

A = k

_{3}/2

P

_{1}= (2k

_{1}/ k

_{3}) +1