4. A biologist observes a population of rabbits regularly over a period of several years. Her observations show that for the first 2 years the population size doubles approximately every six months, from an initial population of 50 rabbits, before levelling off. She suggests the following model for the population in the first 2 years: f ( t) = A(2" ), Osts2 where f (t) is the number of rabbits, t is the time in years and A and k are constants. (a) Give values for A and k , explaining your reasoning carefully. [2] The biologist is interested in how much food is required to sustain the rabbit population. She suggests a model of: g (x) = cx, x>0where g(x) is the number of units of food consumed daily by the population, x is the number of rabbits in the population and c is a constant. (b) Explain what the coefficient of x represents in this model. (c) State one assumption made by the biologist. (d) Explain why the given domain for the function is unlikely to be a good model. (e) Find the composite function gf (t ) in terms of c, stating its domain clearly. Explain what relationship is given by this composite function. [3] (f) Explain why it does not make sense to find the composite function fg(x) . [1]