## Related questions with answers

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?

Solution

VerifiedLet $A$, $B$ denotes the states of being homeowners and renters respectively. The 2000 census reported that 66.4% of the households in Alaska were homeowners, and the remainder $(100-66.4)\%=33.6\%$ were renters. Taking that as initial state, the initial state matrix

$S_0=[\,\,0.664\quad 0.336\,\,]$

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