Chapter 9.1, Problem 89E

Housing trends. The $2000$ census reported that $41.9\%$ of the households in the District of Columbia were homeowners and the remainder were renters. During the next decade, $15.3\%$ of homeowners became renters, and the rest continued to be homeowners. Similarly. $17.4\%$ of 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 $2030$ ?