Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies.
The population distribution after n number of years from the initial year is , where and
We take the limit as n->infinity.
We evaluate lim n->infinity by first finding matrices D and Q such that . So, , where D is a diagonal matrix, whose diagonal entries are eigenvalues of T, and their corresponding eigenvectors are the columns of the matrix Q.
So we have and .
Notice that as n goes to infinity
Hence, as n goes to infinity
Hence, the limiting distribution distribution is =120,000people and =80,000 people.