Consider a three bin population model. That is, the population vector Pk satisfies the difference equation A-S0 0 0 S2 83 where the fi's are the fertility rates and the si's are the survival rates. 0.5 0.8 (a) Suppose f 0.2 and 0.5. Carefully explain why the Gershgorin Circle Theorem gives 0.1 0.4 an upper bound on the spectral radius of p(A) 0.9 and thus limko A* -O. (b Malab) Using the fertility and survival rates given above, use Matlab to plot the eigenvalues of A in the complex plane. On the same plot draw the three Gershorin circles and verify that each eigenvalue of A is contained within one of the Gershorin disks. Use a stacked bar graph in Matlab to plot P for k 0,..., 40 to confirm the population is decreasing to 0