Chapter 2.5, Problem 20P

(a)

To determine

To show: That $\frac{dy}{dt}=r\left(1-y/K\right)y-h$ has two equilibrium points $y_1$ and $y_2$ and determine these points.

(b)

To determine

To show: That the value of $y_1$ is unstable and $y_2$ is asymptotically stable.

(c)

To determine

To show: That if the initial population $y_0>y_1$ by using the given data.

(d)

To determine

To show: That y decreases to zero as t increases by using the given data.

(d)

To determine

To show: That there is a single equilibrium point $y=\frac{K}{2}$.