In a certain region, 6% of a city’s population moves to the surrounding suburbs each year, and 4% of the suburban population moves into the city. A 2019 census measures 10,000,000 residents in the city and 800,000 in the suburbs. (a) Set up a difference equation (of the form ~xn+1 = A~xn) that describes this situation, where ~x0 is the initial population in 2019. (b) Estimate the populations in the city and suburbs two years later, in 2021.

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?