8. Total 10 points. a. [4 points] Given the discrete-time logistic growth model below, compute X2. Assume, Xo = 1, and r = 3.5. XN+1 = rXN(1 -XN)b. [3 points] For different values of r, the above model shows the following behaviors. Identify the type of attractor in each case. X'- r= 2'9 u T = 3.35 n .vVVYHHTYVY'Wln' w}: u ' . 'mmlmmun a. u a m In I) In N c. [3 points] Beginning from the left-most figure, what types of bifurcation must occur to lead to such changes in the behavior? Explain with reference to changes in the parameter r