a population is modeled by a function p that satisfies the differential equation dp/dt = k(1200-p), rest in comments

Question

where t is time in years and k is the constant of proportionality. when t=0, the population is 300 .

(a) find p(t) in terms of t and k.

(b) if p(4) = 600, find the value of k.

(c) find lim t to infinity p(t).

Answer 1

The is a first order linear DE with solution pe^kt = 1200k ∫e^kt dt.

You find the constant of integration from the initial condition and the value of k from part 2.

The limit will be obvious when you have evaluated k and the constant of integration.