Question

In a certain region each person is understood to live either in the city or the suburbs. Each year 6% of the city population moves to the suburb (and the rest stays in the city). Also each year 4% of the suburb population moves to the city (and the rest stay in the suburbs). Suppose that x1 is the number of people who live the city in a certain year, and x2 is the number of people who live in the suburb in that same year. Let y1 be the number of people who live in the city the year after, and similarly y2 be the number who live in the suburbs. (a) Write down a formula for y1 in terms of x1 and x2. Then write down a formula for y2 in terms of x1 and x2.

Answer 1

Answer:

y₁=x₁+0.04x₂

y₂=x₂+0.06x₁

Step-by-step explanation:

In the first year, number of people who live:

In the city= x₁

In the suburb=x₂

New Population in the next year

In the city= y₁

In the suburb=y₂

If each year 6% of the city population moves to the suburb,

New Suburb Population=Previous Population+Immigrants

y₂=x₂+0.06x₁

If each year 4% of the suburb population moves to the city,

New City Population=Previous Population+Immigrants

y₁=x₁+0.04x₂

y₁=x₁+0.04x₂

y₂=x₂+0.06x₁