Chapter D1.2, Problem 23E

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.

23.     $\begin{array}{c}{P}^{\prime }\left(t\right)=0.02P\left(4-\frac{P}{800}\right);P\left(0\right)=1600,P\left(0\right)=2400,\\ P\left(0\right)=4000\end{array}$