Two towns, Avaricia and Covetton, are located on opposite sides of a national park. The two towns are heavily dependent on tourism, and they compete with one another both for the business of tourists coming to the park, and for residents to work in the tourism industry.
Government officials studying the two towns indicate the population of Avaricia by a, and the population of Covetton by c. If the respective populations at a particular point in time are and , then data suggest that the populations one year later may be modelled by the following system of coupled equations:
Let and indicate the respective populations of the two towns at the start of the study.
Use a matrix method to show that the respective populations after years are predicted by the model to be