11. For any positive integer n, the Hassell model of exponent n f(x)=(1+Mx)nRx,M>0,R>1 describes the size f(x) of a population given the size x0 of the population in the previous generation. (The special case n=1 gives the Beverton-Holt model from Assignment 1.) (a) [3 marks] Let n2. Solve the equation f(x)=x. (b) [2 marks] Let n2. Find the horizontal asymptote of f(x). (c) [3 marks] Let n1 and n2 be distinct positive integers. Find all points of intersection between the graphs of the Hassell models of exponent n1 and n2. Answer: (d) [3 marks] Pictured below is a graph of the Beverton-Holt model. On the same set of axes, sketch the graph of a Hassell model of exponent n2. (You may assume that the parameters M and R are the same in both models.) Student number: 15 (e) [3 marks] The exponent n is sometimes interpreted to indicate the degree to which scarce resources are distributed equally in a population. Based on your answers to previous parts of this question, do you think an exponent of n2 corresponds to more equal or less equal distribution of scarce resources, compared to an exponent of n=1 (i.e. the Beverton-Holt model)? Justify your answer in a few sentences