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Question 7 The logistic growth with harvesting model for a population y(t) at time t is given by y'(t) = ay(t) (Ymax y(t)) H Here Ymax is the maximum sustainable population of the environment, a is a constant and H is a constant harvesting rate. For Ymax = 8000, a=0.0001, and H = 1000, using the DEplot command, graph y(t) for 0 STS 10 for the initial values y(0) in 1000, 4000, 8000 and 10000. Now determine populations y for which y'= 0, i.e., find the initial polulations for which there is no growth or decline. You should get two. Graph these on the same graph - you should get two straight lines. Question 7 The logistic growth with harvesting model for a population y(t) at time t is given by y'(t) = ay(t) (Ymax y(t)) H Here Ymax is the maximum sustainable population of the environment, a is a constant and H is a constant harvesting rate. For Ymax = 8000, a=0.0001, and H = 1000, using the DEplot command, graph y(t) for 0 STS 10 for the initial values y(0) in 1000, 4000, 8000 and 10000. Now determine populations y for which y'= 0, i.e., find the initial polulations for which there is no growth or decline. You should get two. Graph these on the same graph - you should get two straight lines

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