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.

(a) With the help of the slope field, discuss what happens to an initial population of 6000 fish. Does it increase or decrease?

(b) How about an initial population of 1000 fish? Does it increase or decrease?

(c) On the slope field in Fig. 9 or a copy of it, draw the solution of the initial-value problem y′ = 0.1y (5 - y), y (0) = 1. What does this solution represent?

Transcribed Image Text:

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