A study of the antelope population in a wildlife park has shown that antelope regularly move between three locations, east (`E`), north (`N`) and west (`W`).
Let `A_n` be the state matrix that shows the population of antelope in each location `n` months after the study began.
The expected population of antelope in each location can be determined by the matrix recurrence rule
`A_(n + 1) = T A_n - D`
where
`{:(),(),(T=):}{:(qquadquadtext(this month)),((qquadE,quadN,quadW)),([(0.4,0.2,0.2),(0.3,0.6,0.3),(0.3,0.2,0.5)]):}{:(),(),({:(E),(N),(W):}):}{:(),(),(text(next month)):}`
and
`D = [(50),(50),(50)]{:(E),(N),(W):}`
The state matrix, `A_3`, below shows the population of antelope three months after the study began.
`A_3 = [(1616),(2800),(2134)]{:(E),(N),(W):}`
The number of antelope in the west (`W`) location two months after the study began, as found in the state matrix `A_2`, is closest to
- 2060
- 2130
- 2200
- 2240
- 2270