Problem 4.2 (Textbook: Problem 2.3.10 on P91): Suppose that the fish population P(t) in a lake is attacked by a disease (such as human being who eats them) at time t = 0, with the result that the fish cease to reproduce (so that the birth rate is ß = 0) and the death rate 8 (deaths per week per fish) is thereafter proportional to P-2. If there were initially 10,000 fish in the lake and 199 were left after 19 weeks, how long did it take for the lake to contain 0 fish? Can you change the "199" to a different number such that the fish count never changes with time? To what number if so?

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Differential Calculus

**Problem 4.2** (*Textbook: Problem 2.3.10 on P91*): Suppose that the fish population \( P(t) \) in a lake is attacked by a disease (such as a human being who eats them) at time \( t = 0 \), with the result that the fish cease to reproduce (so that the birth rate is \( \beta = 0 \)) and the death rate \( \delta \) (deaths per week per fish) is thereafter proportional to \( P^{-\frac{1}{2}} \). If there were initially 10,000 fish in the lake and 199 were left after 19 weeks, how long did it take for the lake to contain 0 fish? Can you change the “199” to a different number such that the fish count never changes with time? To what number if so?
Transcribed Image Text:**Problem 4.2** (*Textbook: Problem 2.3.10 on P91*): Suppose that the fish population \( P(t) \) in a lake is attacked by a disease (such as a human being who eats them) at time \( t = 0 \), with the result that the fish cease to reproduce (so that the birth rate is \( \beta = 0 \)) and the death rate \( \delta \) (deaths per week per fish) is thereafter proportional to \( P^{-\frac{1}{2}} \). If there were initially 10,000 fish in the lake and 199 were left after 19 weeks, how long did it take for the lake to contain 0 fish? Can you change the “199” to a different number such that the fish count never changes with time? To what number if so?
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