Refer to the differential equation in Exercise 39.

(a) Obviously, if you start with zero fish, f(t) = 0 for all t. Confirm this on the slope field. Are there any other constant solutions?

(b) Describe the population of fish if the initial population is greater than 5000; less than 5000. On the slope field in Fig. 9 or a copy of it, draw solution curves to illustrate your description.

Exercise 39

Let f (t) denote the number (in thousands) of fish in a lake after t years, and suppose that f (t) satisfies the differential equation y′ = 0.1y (5 - y). The slope field for this equation is shown in Fig. 9.

6 5 4 3 y (in thousands) 2- 1 1 1 \\\\\\\\\\\\\ 0 1 Figure 9 // 2 / 3 1 17 1 4 5 6 / t