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**1. Homework Statement**

Suppose that when a certain lake is stocked with a population P of fish, the birth and death rates [tex]\alpha[/tex] and [tex]\beta[/tex] are inversely proportional to [tex]\sqrt{P}[/tex] , so that

[tex] \frac{dP}{dt} = k \sqrt{p} [/tex]

Find P(t) if P(0)=C

**3. The Attempt at a Solution**

[tex] \frac{dP}{\sqrt{p}} = k dt [/tex]

integrate

[tex] 2 \sqrt{P} = k t + A [/tex]

Sub 0 for t C for X

[tex]A=2 \sqrt{C}[/tex]

sub back in

[tex] 2 \sqrt{P} = 2t+4 \sqrt{c} [/tex]

[tex] P = (2 t k+4 \sqrt{C})^2 [/tex]

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