Chapter 10.2, Problem 40E

(a)

To determine

The constant solution of $y\text{'}=0.1y(5-y)$ with the help of the slope field, where $f\left(t\right)$ denotes the number of fish in lake and $f\left(t\right)$ is the solution of $y\text{'}=0.1y(5-y)$. The slope field is given as below.

(b)

To determine

The population of fish if the initial population $f\left(t\right)>5000$ or $f\left(t\right)<5000$, where $f\left(t\right)$ denotes the number of fish in lake and $f\left(t\right)$ is the solution of $y\text{'}=0.1y(5-y)$. The slope field is given as below.