A new mass transit system has gone into operation. The transit authority has made studies that predict the percentage of commuters who continue driving their car or will change to mass transit or riding a bicycle. Their studies show that: 15% of commuters using a car will switch to mass transit and 5% will start riding a bike; 30% of the commuters currently using the mass transit will start driving a car and 5% will start riding a bike; 10% of the commuters currently riding a bike will switch to mass transit and 20% will start driving a car. Suppose that the population of the area remains constant, and that currently 25% of the commuters will use mass transit, 70% use their cars and 5% bike.
a) What percentage of the commuters will be using mass transit after 1 year? After 2 years?
b) What percentage of commuters will be using the mass transit in the long run? Explain the relevance of the dominant eigenvector in answering such a question.
c) Can the transit company expect that the percentage of commuters driving a car will drop below 50% in the future?