Chapter 9.1, Problem 53E

a.

To determine

To verify: The given function $P\left(t\right)=\frac{K}{1+C{e}^{-rt}}$ is a solution of the differential equation $P^{\prime }\left(t\right)=rP\left(1-\frac{P}{K}\right)$.

b.

To determine

To find: The value of C.

c.

To determine

To sketch: The graph of the solution when $P\left(0\right)=50,r=0.1$ and $K=300$.

d.

To determine

To find: The value of $\underset{t\to \infty }{\lim }P\left(t\right)$.