Age Distribution There are two age groups for a particular species of organism. Group I co...

Age Distribution There are two age groups for a particular species of organism. Group I consists of all organisms aged under 1 year, while group II consists of all organisms aged from 1 to 2 years. No organism survives more than 2 years. The average number of offspring per year born to each member of group I is 1, while the average number of offspring per year born to each member of group II is 2. Nine-tenths of group I survive to enter group II each year.

(a) Let x and y represent the initial number of organisms in groups I and II, respectively. Let a and b represent the number of organisms in groups I and II, respectively, after one year. Write a matrix equation relating  to. .

(b) If there are initially 450,000 organisms in group I and 360,000 organisms in group II, calculate the number of organisms in each of the groups after 1 year and after 2 years.

(c) Suppose that, at a certain time, there were 810,000 organisms in group I and 630,000 organisms in group II. Determine the population of each group 1 year earlier.