Consider a human population that is divided into three age classes; those aged 0–15 years, those aged 15–30 years, and those aged 30–45 years. The Leslie matrix for the female population is given by L =

⎛

⎝

0 1 0.5 0.9 0 0 0 0.8 0

⎞

⎠.

Given that the initial population distribution of females is x(0)

1 = 10,000, x(0)

2 = 15,000, and x(0)

3 = 8000, compute the number of females in each of these groupings after

(a) 225 years;

(b) 750 years;

(c) 1500 years.