Question

a) Within a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 40% of those now using public transportation will commute via automobile and 60% will continue to use public transportation. In the long run, what percentage of the commuters will be using public transportation? (Round your answer to the nearest percent.)

_____%

b)

Find the steady-state vector for the transition matrix.

	0.6	0.1	0.1
	0.4	0.8	0.4
	0	0.1	0.5

________

x= ________

________

Answer 1