Problem #2: Suppose there is a fish population of size PCt) Cin thousands) that

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Problem #2: Suppose there is a fish population of size PCt) Cin thousands) that grows according to the logistic model, but from which fish are harvested for 6 months of every year. The variable t is measured in months. The population grows according to dP POP Harvest t) where k 0.011, and P 00, the maximum carrying capacity. Harvesting is done 6 months of the year, so that Harvest(t) H [sin ns 1] (2Jat/12) where H-32. There is an initial condition that P(0) 86. The harvest function is a way of producing a continuously differentiable function that is pretty close to periodically turning on DHarvest(t) 32] and off [Harvest(t) 0 every 6 months Produce a graph of the function Harvest t) on the interval 0 s t s 24. Use your First Name, Last Name, and Student Number as the title for the graph (e.g., Johnny Good, 1234567). Then save the graph as a png file and upload it Note: Fractional exponents of negative numbers are tricky, and attract consideration of complex numbers. To get the real-valued "15th root" of u, where u is an expression dike sin that could possibly be negative, use nth root (u, 15).

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