A lake is stocked with 100 fish. Let f (t) be the number of fish after t months, and suppose that y = f (t) satisfies the differential equation y′ = .0004y(1000 - y). Figure 7 shows the graph of the solution to this differential equation. The graph is asymptotic to the line y = 1000, the maximum number of fish that the lake can support. How fast is the fish population growing when it reaches one-half of its maximum population?

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1000 800 600 400 200 y + 5 10 Figure 7 Growth of a fish population. 15