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Algebra

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Of two-car families in a small city, 88% remain two-car families in the following year and 12% become one-car families in the following year. Of one-car families, 72% remain one-car families and 28% become two-car families. Suppose these trends continue for a few years. At present, 4800 families have one car and 4200 families have two cars.
Find the numbers of one-car familes and two car families two years from now.

  • Algebra - ,

    I assume you are learning about Markov's chains in the study of matrices

    end of year 1:
    [4200 4800] x

    .88 .12
    .72 .28
    =
    [7152 1848]

    end of year 2
    [7152 1848]
    .88 .12
    .72 .28
    =
    [7624.32 1375.68]

    I am not absolutely sure if I have the correct order, haven't done this kind of math in almost 20 years.

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