ASSIGNMENT 1 For a particular species, the model f(x) = 1+ x/M' Rx M>0,R>1 describes the size f(x) of a population given the size x of the population in the previous generation. Because x represents a population, the domain is restricted to x ? 0. 1. (a) Solve f(x) = x. (b) Describe in a paragraph what the solution(s) found in part (a) represent, in terms of populations. 2. (a) What polynomial function approximates f(x) well for large values of x? Explain your reasoning. (b) In a paragraph, interpret your answer in part (a) in terms of populations. What does your answer tell you about how this model describes populations? 3. (a) What polynomial function approximates f(x) well for small values of x? Explain your reasoning. (b) In a paragraph, interpret your answer in part (a) in terms of populations. What does your answer tell you about how this model describes populations, and what is the significance of the constant R? 4. (a) It may be shown that f'(x) = (M+x)z, which is always positive. Describe in a paragraph what the feature f'(x) > 0 for all x > 0 implies, in terms of population. (b) Why might the feature f'(x) > 0 for all x ? 0 be unsuitable for modelling certain populations? Describe your answer in a few sentences.