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.

Question

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.

Reiny · Answer

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.