Chapter 9.1, Problem 96E

Housing trends. The $2000$ census reported that $66.4\%$ of the households in Alaska were homeowners, and the remainder were renters. During the next decade, $37.2\%$ of the homeowners became renters, and the rest continued to be homeowners. Similarly, $71.5\%$ of the renters became homeowners, and the rest continued to rent.

(A) Write the appropriate transition matrix.

(B) According to this transition matrix, what percentage of households were homeowners in $2010$ ?

(C) If the transition matrix remains the same, what percentage of households will be homeowners in $2030$ ?