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  3. 2 consider the following mathematical model of a fishery assume...

Question: 2 consider the following mathematical model of a fishery assume...

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2. Consider the following mathematical model of a fishery. Assume that fish are caught at a constant rate h independent of the size of the fish population y(t). Then y satisfies dy/dt-(1- y/K)y - h where r and K are positive constants. (a) If h < rK/4, show that equation (1) has two equilibrium points y and y2, with yi < 2: determ (b) Show that yı is unstable and уг is asymptotically stable (c) Show that if the initial population o>yi, then y ast, but that if yo < then y decreases as t increases. Note that y = 0 is not an equilibrium point, so if yo < yl, then extinction will be reached in a finite time (d) If h > rK/4, show that y decreases to zero as t increases regardless of the value of yo (e) If hrK/4, show that there is a single equilibrium point y K/2 and that this point is semistable. Thus the maximum sustainable yield is hm rK/4, corresponding to the equilibrium value y- K/2. The fishery is considered to be overexploited if y is reduced to a level below K/2. nine these points. 3. Determine whether each of the following equations is exact. If it is exact, find the solution
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