Answer Happy

4. Make the following simplification in the cohort model of age distribution: woman have children between the ages of 13 and 38 inclusive; each woman has exactly one female child; each woman lives to be at least 39 years old. Using a time interval of 13 years with these assumptions, and considering only those females less than 39 years old, gives the following model: 1-a X1 (k + 1) X2 (k+1) X3 (k + 1) о а 1 0 = 0 0 X1 (k) X2 (k) *3 (k) 0 1 where 0 <a < 1. (a) Find the eigenvalues. Find the dominant eigenvalue and the corresponding eigenvector. (b) Determine the growth rate. (c) How quickly does the population move to equilibrium? [The answer depends on the value of a.]