Could you please answer question 4?

A researcher is modelling the evolution of a companys market share in time using the function f (x) = Rx 1 + M x . Here x represents the companys market share in a particular year, and f (x) the market share in the following year (test your understanding: what would f (f (x)) represent?). The parameters R, M (which depend on the company and its relationship to the market) satisfy M > R 1 > 0. Since x represents a proportion of the market, the domain of f is the interval [0, 1]. 1. (a) Solve the equation f (x) = x. (b) Describe in a paragraph what the solution(s) found in part (a) represent, in terms of market shares. 2. (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 market shares: what does your answer to part (a) tell you about how this model describes companies with small market share? what is the significance of the constant R? (recall the assumption R > 1) 3. (a) It may be shown that f (x) = R (1+Mx)2, which is always positive. Describe in a paragraph what the feature f (x) > 0 for all x 0 implies, in terms of market shares. (b) Why might the feature f (x) > 0 for all x 0 be unsuitable for modelling certain market situations? Describe your answer in a few sentences. 4. Suppose instead that 0 < R < 1. (a) How would your answer to question 1(a) change? (b) How would your answer to question 1(b) change? (c) How would your answer to question 2(b) change?