Question

A population of animals in an ecological niche is growing in time so that it's rate of growth dp/dt is related to its current size by the differential equation dp/dt = 900/p^2. If time is measured in years and initially there are P(0) = 10 animals present, find the population function P(t) giving the size of the population after t years.

Answer 1

If dp/dt = 900/p^2, you can solve that differential equation using separation of variables

Integral of p^2 dp = Integral or 900 dt
p(0) to p(t) ........ = 0 to t

900 t = p(t)^3/3 - p(0)^3/3
p(t)^3 = p(0)^3 + 2700 t = 1000 + 2700 t

Solve for p(t)

Answer 2

Note the growth is not exponential in this case. It is much slower than that, approaching t^(1/3) growth as t goes to infinity