The density of fish (i.e. the number of fish per cubic metre) in a lake is...

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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) 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)