Exercise A. Consider a fish population in a lake. Let us assume that this fish population has a logistic growth. We moreover assume that shermen catch a percentage d of the sh per unit of time. The model is thus X " = TX (1 g) dX. To make computations simpler, we assume that r = k = 1. The model thus becomes X' = X (1 X) 05X. Sketch the phase portraits for d = 0, 03,06,053, 1 and use them to create a bifurcation diagram for this system. (Unlike what we normally do for population models, also use negative numbers for X when necessary). Hint: To make your computations simpler, you can factor X out to the equation of the modet