Question

FF3:38 3A23B 57% . Grades (1 point) Hassell's model is often used to study populations of insects. Suppose that the updating function for the population of a species of moth P in a sample plot is given by Problems 0.003P)2 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 a. Let the initial population Po 10. Find the population of the next three years, P45 101+0.00 P24545 101+C b. Find all non-negative equilibria for this Hassell's model. (Ple Pe Equilibria are Pie c. The updating function (or the iterated map from our course notes) for this model is and P2 (3000 5"0.5-1 45P HP) +0003P Find the derivative of the updating function. H'(P)45 (1+0.003P)"2-(0.006+0.003 0.003 2P) 45P1+0 The P-intercept of the updating function (i.e., the value of P for which H(P-0) is 0 The maximum of the updating function has the coordinates P0.54+0.0729 and HP There is a horizontal asymptote at H You should sketch a graph of the updating function with the identity map, P,+ d. Evaluate the derivative at the equilibria and use the value to determine the stability of that equilibrium point H'(Pie) so this equilibrium is Stable or Unstable so this equilibrium is Stable or Unstable

Answer 1