Science:Math Exam Resources/Courses/MATH152/April 2016/Question B 04 (d)/Solution 1

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We first use the Matrix diagonalization method to write the matrix in the following form:

where and

From part (a) and (c), we have and Also, and So, we have and therefore,

We finally get that

which means for any time we have

Now we are ready to find for large by computing So,


Now by applying this matrix on our initial population we get

Therefore, million people will be living in the suburbs far in the future.