Mathematical ecologist have created a mathematical model toanalyze population dynamics of the northern spotted owl by dividingthe female owl population into three categories: juvenile (up to 1year old), sub-adult (1 to 2 years), and adult (over 2 years old).By analyzing these three subgroups, it is possible to use thenumber of females in each subgroup at time n to estimate the numberof females in each group at any time n+1 with the following matrixequation:
where j(n) is the number of juveniles, s(n) is the number ofsubadults, and a(n) is the number of adults at time n.
If there are currently 500 female northern spotted owls made upof 900 juveniles, 500 subadults, and 2600 adults. What is the totalnumber of females owls for each of the next 5 years?