3. We have been exploring how the continuous) logistic differential equation and (discrete) logistic difference equation can have extremely dissimilar dynamics. A discrete model, known as the Beverton-Holt equation, that more closely aligns with the simple dynamics seen in the logistic differential equation may be written as follows: In+1 rin 1+ in n=0,1,..., r > 0, 3 > 0. (a) This nonlinear equation is surprisingly solvable when to > 0. Take the reciprocal of both sides and make the substitution Yn 1 In (b) Find an explicit solution for the resulting equation (by solving for yn in terms of yo). Then translate your solution to express Xn in terms of 20 > 0. (c) We have previously seen that the original equation has a sink at I + =r-1 for r > 1. Find the largest possible basin of attraction of this fixed point (for r > 1). Here zo > 0. (Hint: Find lim In from the solution in part (b). What dependence is there on ro?) n->00 3. We have been exploring how the continuous) logistic differential equation and (discrete) logistic difference equation can have extremely dissimilar dynamics. A discrete model, known as the Beverton-Holt equation, that more closely aligns with the simple dynamics seen in the logistic differential equation may be written as follows: In+1 rin 1+ in n=0,1,..., r > 0, 3 > 0. (a) This nonlinear equation is surprisingly solvable when to > 0. Take the reciprocal of both sides and make the substitution Yn 1 In (b) Find an explicit solution for the resulting equation (by solving for yn in terms of yo). Then translate your solution to express Xn in terms of 20 > 0. (c) We have previously seen that the original equation has a sink at I + =r-1 for r > 1. Find the largest possible basin of attraction of this fixed point (for r > 1). Here zo > 0. (Hint: Find lim In from the solution in part (b). What dependence is there on ro?) n->00