Problem 2E

In a certain region, about 6% of a city’s population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2010, there were 10,000,000 residents in the city and 800,000 in the suburbs. Set up a difference equation that describes this situation, where x0 is the initial population in 2010. Then estimate the populations in the city and in the suburbs two years later, in 2012.

Answer:

Step 1:

In this problem we need to Set up a difference equation that describes given situation and we have to estimate the populations in the given city and in the suburbs two years later , in 2012.

Given : of a city’s population moves to the surrounding suburbs each year.

of the suburban population moves into the city.

is the initial population in 2010.

In 2010 number of residents in the city is :

In 2010 number of suburbs in the city is :