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In a certain region, about 7$\%$ of a city's population moves to the surrounding suburbs each year, and about 5$\%$ of the suburban population moves into the city. In 2015 , there were $800,000$ residents in the city and $500,000$ in the suburbs. Set up a difference equation that describes this situation, where $\mathbf{x}_{0}$ is the initial population in 2015 . Then estimate the populations in the city and in the suburbs two years later, in 2017 . (Ignore other factors that might influence the population sizes.)

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 10

Linear Models in Business, Science, and Engineering

Introduction to Matrices

Campbell University

Oregon State University

McMaster University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

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For the following exercise…

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Many factors may contribut…

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Okay, so, you know, this property were used. Difference in question. Um, so if you find a difference a question illiterate, you creatively. So accept a pass. One equals two. A transition matrix in terms except came and the X zero in this case, the initial state will be the initial population in the city and the suburban. Our area in the transition met a traditional metrics will be a following. So the reason we have this tradition, megs are metrics. Is that because, um so for each year, about 7% 7% off the population moves to the surrounding suburban area for on the city and the for. Each year we have about 5%. People move back towards the city, and the first population is for the city. And the second in training this egg zero, your be the step. All right. Okay, So after two years, we are looking for eggs, too. X two equals two in terms eggs one. And the recursive lee X one equals tour. Um, sometimes eg zero. Um, so in the end, we have and square tents and x zero So back calculator. The result will be on this. So after two years. This is a population in city and then and that this is the population for the surrounding separate. So this is a solution to this problem.

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