Using Matrix Products to Predict Population Distribution

Question

Suppose that, for a certain metropolitan area and the surrounding country, during each 5-year period an average of 30% of the metropolitan population M moves to the surrounding counties and the rest remains. Similarly, suppose that in the same period, an average of 20% of the surrounding counties' population S moves to the metropolitan area and the rest remains. This population dynamic can be represented by the following matrix, where row 1 shows how the metropolitan population M changed (70% remained in M and 30% moved to S), and for row 2 shows how the population of the surrounding counties changed.

Currently the population is evenly divided between the two areas, which can be represented by the row matrix shown below.

Predictions of this population distribution after 10 years and after 15 years could be found from what matrix products?

Summary:The question belongs to Mathematics and it is about predicting population distribution of a metropolitan area using matrix products

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