Acertain species of insect can be divided into three age classes: 0–6 months, 6–12 months, and 12–18 months. A Leslie matrix for the female population is given by L =

⎛

⎝

0 4 10 0.4 0 0 0 0.2 0

⎞

⎠.

Determine the long-term distribution of the insect population.An insecticide is applied which kills off 50% of the youngest age class. Determine the longterm distribution if the insecticide is applied every six months.