Question: A new rapid transit system has just started operating. In the first month of operation, it is found that 25 percent of the commuters are

A new rapid transit system has just started operating. In the first month of operation, it is found that 25 percent of the commuters are using the system, while 75 percent still travel by automobiles. The following transition matrix was determined from records of other rapid transit systems:

Of those currently using the new system, 80% will continue using the system

Of those currently using automobiles, 30% will change to the new system

What is the initial state matrix?

What percentage of the commuters will be using the new system after 1 month?

After 2 months?

Find the percentage of commuter using each type of transportation after it has been in service for a long time.

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