Table 4 gives the percentage of the U.S. population living in the northeast region during the indicated years.

The following transition matrix P is proposed as a model for the data, where N represents the population that lives in the northeast region:

(A) Let S0 = [.241 .759] and find S1, S2, and S3. Compute the matrices exactly and then round entries to three decimal places.
(B) Construct a new table comparing the results from part (A) with the data in Table 4.
(C) According to this transition matrix, what percentage of the population will live in the northeast region in the long run?

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Table 4 1970 1980 1990 2000 Percent 24.1 21.7 20.4 19.0 Next decade Current N [.61 39 decade N' 1.09 91