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 4200have two cars.

a. Draw a transition diagram that displays this information.
b. What matrix represents the present situation? Let a11 represent one-car families that remain one-car families.
c. Write a transition matrix that represents the same information as your transition diagram.
d. Write a matrix equation to find the numbers of one-car and two-car families one year from now.
e. Find the numbers of one-car and two-car families two years from now.