The population of a colony of bacteria grows in such a way that the population size at any

hour t is the sum of the populations of the 3 previous hours. Suppose that the matrix

describes the population sizes for 3 successive hours.
(a) Write matrix M so that MN gives the population sizes for 3 successive hours beginning 1 hour later-that is, such that

(b) If the populations at the ends of 3 successive 1-hour periods were 200 at the end of the first hour, 370 at the end of the second hour, and 600 at the end of the third hour, what was the population 1 hour before it was 200? Use M-1.
Set up each system of equations and then solve it by using inverse matrices?

Transcribed Image Text:

n, N= n+1 ++1 MN = n42 n, + n,+1+ M,+2-