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In a certain region, about 7% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2017, there were 1,150,000 residents in the city and 550,000 residents in the suburbs. a) Set up a difference equation (in the form of a matrix equation X, = MX,) that describes this situation, where X, is the initial population in 2017. b) Estimate the populations in the city and in the suburbs two years later, in 2019. (Ignore other factors that might influence the population sizes.)

In a certain region, about 7% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2017, there were 1,150,000 residents in the city and 550,000 residents in the suburbs. a) Set up a difference equation (in the form of a matrix equation X, = MX,) that describes this situation, where X, is the initial population in 2017. b) Estimate the populations in the city and in the suburbs two years later, in 2019. (Ignore other factors that might influence the population sizes.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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4) Read the section in your book on difference equations and answer the following questions. In a certain region, about 7% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2017, there were 1,150,000 residents in the city and 550,000 residents in the suburbs. a) Set up a difference equation (in the form of a matrix equation X, = MX,) that describes this situation, where X, is the initial population in 2017. b) Estimate the populations in the city and in the suburbs two years later, in 2019. (Ignore other factors that might influence the population sizes.)
Transcribed Image Text:4) Read the section in your book on difference equations and answer the following questions. In a certain region, about 7% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2017, there were 1,150,000 residents in the city and 550,000 residents in the suburbs. a) Set up a difference equation (in the form of a matrix equation X, = MX,) that describes this situation, where X, is the initial population in 2017. b) Estimate the populations in the city and in the suburbs two years later, in 2019. (Ignore other factors that might influence the population sizes.)
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