Population of Fish in a Lake A lake is stocked with 100 fish. Let f(1) be the number of fish after i months, and suppose that y = f(1) satisfies the differential equation y' = .0004y(1000 – y). Figure 7 shows the graph of the solu- tion 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? 1000 800 600 400 200 10 15 Figure 7 Growth of a fish population.

Survey Of Economics
10th Edition
ISBN:9781337111522
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter1: Introducing The Economic Way Of Thinking
Section1.A: Applying Graphs To Economics
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Population of Fish in a Lake A lake is stocked with 100
fish. Let f(1) be the number of fish after i months, and
suppose that y = f(1) satisfies the differential equation
y' = .0004y(1000 – y). Figure 7 shows the graph of the solu-
tion 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?
1000
800
600
400
200
10
15
Figure 7 Growth of a fish population.
Transcribed Image Text:Population of Fish in a Lake A lake is stocked with 100 fish. Let f(1) be the number of fish after i months, and suppose that y = f(1) satisfies the differential equation y' = .0004y(1000 – y). Figure 7 shows the graph of the solu- tion 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? 1000 800 600 400 200 10 15 Figure 7 Growth of a fish population.
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