Use matrices to solve applications in which a sequence of events repeats itself over a period. For instance, the following application is from the field of botany.

A biennial plant matures 1 year after a seed is planted. In the second year, the plant produces seeds that will become the new plants in the third year, and then the 2-year-old plant dies. Suppose that a wilderness area currently contains 500,000 of a certain biennial and that there are 225,000 plants in their first year and 275,000 in their second year. Suppose also that 70% of the 1-year-old plants survive to the second year and that each

1000 second-year plants give rise to 1400 new first-year plants. See Figure

70% First-year plants Second-year plants 140% Yearly transition diagram for biennial plants