1. Consider the Ricker model for the population of Atlantic cod: f(S) = ase-$/b Here, S is the cod population this year, f(S) is the population of cod next year and a and b are positive constants. (a) Calculate the derivative, f'(S). (b) Evaluate f'(0) and explain what it represents, making sure to include units. (c) Determine the intervals where f(S) is increasing and decreasing on the domain [0, co). (d) How would a change in a affect the intervals of increase and decrease? (e) How would a change in b affect the intervals of increase and decrease? (f) Determine where the rate of change of the future population of cod is decreasing the fastest