Chapter D1.2, Problem 24E

Logistic equations Consider the following logistic equations, for t ≥ 0. In each case, sketch the direction field, draw the solution curve for each initial condition, and find the equilibrium solutions. A detailed direction field is not needed. Assume t ≥ 0 and P ≥ 0.

24.     $\begin{array}{c}{P}^{\prime }\left(t\right)=0.05P-0.001P^2;P\left(0\right)=10,P\left(0\right)=40,P\left(0\right)=80\\ P\left(0\right)=4000\end{array}$