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.
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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e38faf1-cf5c-4007-bf96-7e3f08f52e4b%2F9bd9e8fc-1c24-4a54-b873-df37be773047%2Fxm38298_processed.png&w=3840&q=75)
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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