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# (Solved): Let P(t) denote the population (in hundreds) of fish at a lake at year t. The population dynamics ar ...

Let P(t) denote the population (in hundreds) of fish at a lake at year t. The population dynamics are modeled by the following ODEdPdt=(r0-r1P)P-aPwherer0=5 (in hundreds) is the growth rate under no constraints over resources;-r1P, for some r10, is the term in the growth rate that accounts for limited resources, and thus decreases proportionally as the population grows;a=1 (in hundreds) is the death rate.Instuctions:(a) Determine what should r1 be so that the limiting population is Pe=4 (in hundreds); .(b) Suppose, additionally, that we harvest 300 fish a year, i.e., we have a harvesting rate of h=3.Calculate d/dp (c) Solve for the (explicit) particular solution satisfying the ODE in part (b) and the initial condition P(0)=2.

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