The U.S. Census Bureau published the home ownership rates given in Table 2.

The following transition matrix P is proposed as a model for the data, where H represents the house holds that own their home.

(A) Let S0 = [.433 .567], 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 1.
(C) According to this transition matrix, what percentage of the U.S. female population will be in the labor force in the long run?

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Table 2 Year 1996 2000 2004 Percent 65.4 67.4 69.0 Four years later Current H .95 05 year H 15 85