Consider a population that grows according to the logistic updating function and is harvested at a constant rate h0. The number of individuals per square kilometer of the species satisfies the DTDS +1=x+(3.2-x)-hat a) Give the updating function for this DTDS. This depends on the parameter h. Answer: f(x)= BM b) Determine all equilibrium points of the DTDS. Your answers may depend on the parameter h. List your equilibrium points separated by semi-colons. Answer: c) Determine conditions on h such that all equilibrium points are biologically relevant. Answer: 0 g) Write the formula for the yield of the harvest (rate times population) at the nonzero equilibrium point. Answer: Y(h) = h) Compute the derivative of Y(h) with respect to h. Answer: Y' (h) = i) Determine the value H of h that maximizes the yield and justify your answer. Answer: H= Number because Y' (h) > 0 for 0