Chapter 9.4, Problem 16E

To determine

(a)

To sketch:

The slope field of $\frac{dP}{dt}=-kP\left(1-\frac{P}{B}\right)$.

To determine

(b)

To prove:

$P(0)>B$ if $C>1$ and $0<P\left(0\right)<B$ if $C<0$.

To determine

(c)

To show:

The equation $\frac{dP}{dt}=-kP\left(1-\frac{P}{B}\right)$ models an extinction-explosion population.

To determine

(d)

To show:

$P=0$ is a stable equilibrium and $P=B$ is an unstable equilibrium.