Hello. Could someone solve (i), (ii) and (iii)?

Thanks. Please explain clearly and step by step.

- I. Consider the following density-dependent population model R In+1 = In In +1 where R > 0 is a growth parameter. In other words, the per-capita net growth rate is given R by r(x) 1 and the evolution rule is given by the function 3+1 g(x) for x > 0, so In+1 = g(2n). 2+1 Similarly to the analysis done for the logistic model, answer the following questions: (i) Sketch the graph of r(x), x > 0 and briefly compare it to that from the constant growth rate model Xn+1 Rxn, for which the growth rate is r = R-1. (ii) Determine the fixed points (steady states) by solving the equation g(x) = x, and decide whether they are stable or unstable in terms of parameter R. (Use the first derivative test.) (iii) For each stable fixed point, use the cobwebbing technique to estimate its basin of attraction (the set of all initial values xo > 0 that get attracted by a stable fixed point). - I. Consider the following density-dependent population model R In+1 = In In +1 where R > 0 is a growth parameter. In other words, the per-capita net growth rate is given R by r(x) 1 and the evolution rule is given by the function 3+1 g(x) for x > 0, so In+1 = g(2n). 2+1 Similarly to the analysis done for the logistic model, answer the following questions: (i) Sketch the graph of r(x), x > 0 and briefly compare it to that from the constant growth rate model Xn+1 Rxn, for which the growth rate is r = R-1. (ii) Determine the fixed points (steady states) by solving the equation g(x) = x, and decide whether they are stable or unstable in terms of parameter R. (Use the first derivative test.) (iii) For each stable fixed point, use the cobwebbing technique to estimate its basin of attraction (the set of all initial values xo > 0 that get attracted by a stable fixed point)