Let N(t) be the population of fish (measured in millions of fish) in a lake at time t (measured in years). Suppose that the lake has carrying capacity K (in millions of fish), and that H million fish are harvested from the lake each year. Then N satisfies is the following modification of the logistic equation, for some constant r.

dN /dt = f(N) = rN (K − N/ K) − H.

For all parts of this problem, we use the numbers K = 4 and r = 4 and H=3.75

1. Before allowing the harvest of 3, 750, 000 fish per year, the Department of Fisheries and Oceans must check that there are enough fish in the lake, so that the fishing will not cause the fish population to collapse. How many fish should be in the lake before allowing the harvest of 3, 750, 000 fish per year

2.As H continues to increase, the fish population is at risk of collapsing. This is what happened to Atlantic Cod in Eastern Canada. What is the smallest value of H that guarantees that the fish population will collapse, regardless of the initial population of fish?

pur-new-sol

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