The solid waste generated each year in the cities of the US is increasing. The solid waste generated, in millions of tons, was 205.2 in 1990 and 220.2 in 1998.

Question

1. (a) Assume that the amount of solid waste generated by US cities is a linear function of time. Find a
2. formula for this function by finding the equation of the line through these two points.
3. (b) Use this formula to predict the amount of solid waste generated in the year 2020.
4. (c) How reliable is the prediction for the waste generated in 2020?

Answer 1

slope = rise over run = (220.2 - 205.2)/(1998-1990) = 15/8

Population - 205.2 = (15/8)(x-1990)

P = 15x/8 - 15(1990)/8 + 205.2

P = 15x/8 - 3731.25 +205.2

P = 15x/8 - 3526.05

P in year 2020 = 15(2020)/8 -3526.05

= 261.45 million tons of waste in year 2020

the longer the extrapolation the less reliable