The density of fish (i.e. the number of fish per cubic metre) in a lake is determined by the discrete-time dynamical system 7xt xt+1 1+2x/4 where t is the time in years since the beginning of the observation. Initially, the density is x = 0.3. a) What will the density be after four years? Give your answer with an accuracy of three decimal places. Answer: x4 Number = b) What is the updating function f(x)? Answer: f(x) = c) What are the biologically relevant equilibria? Separate each value by a semi-colon. Answer: d) Compute f'(x). Answer: f'(x) = 05 e) Use the derivative test to determine the stability properties for each of the two equilibria you found in (c). Answer: If p is the smaller equilibrium point, we have f'(p) = Number and so it is Click for List Click for List POT If P is the larger equilibrium point, we have f'(P) = Number and so it is Click for List because Click for List because (give your answer with an accuracy of three decimal places)