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: X₁ (K + 1) 0 α 1-a X₁ (k) X₂ (K + 1) = 10 0 X₂ (k) X3 (K + 1) 01 0 X3 (k) 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.]