# Modeling Population Growth

So I have an equation to describe population growth

where a and b are constants. Typically b is small so that initially, since the population p(t) is small, the squared term can be neglected and the population growth is exponential.

how do I solve the differential equation for p(t) with p(t = 0) = 1 where a = 2 and b = 0.05 and how do I find the value of p(t) as t → ∞

• Is this a math question or a question about how to solve this using Wolfram Mathematica? – Chris K Oct 23 '20 at 23:51
• This DE is separable so you have $$\frac{dp}{p(a+b p)} = dt$$ – Cesareo Oct 24 '20 at 10:29
• If $p$ has an asymptote, necessarily $ap-bp^2=0$ so either $p=0$ or $p=b/a$. – anderstood Oct 24 '20 at 12:23

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