Question

In 1993, Americans recycled 43.8 million tons of solid waste. In 2001, the figure grew to
68.0 million tons. Let N (t) = the number of tons recycled, in millions, and t = the number of years since 1993.

Answer 1

. In 1993, Americans recycled 43.8 million tons of solid waste. In 2001, the figure grew to
68.0 million tons. Let N (t) = the number of tons recycled, in millions, and t = the number of years since 1993.

a) Find a linear function that fits the data

Answer 2

The number of years from 1993 to 2001 = 8
The increase from 1993 to 2001 = 24.2 -- 68.0-43.8 = 24.2
24.2/8 = 3.025 increase per year

Therefore, the function is: N(t) = 3.025t + 43.8
where t=0 for the year 1993, t=1 for the year 1994, t=2 for the year 1995, etc.

You can check this by the following:

N(t) = 3.025t + 43.8
N(8) = (3.025)(8) + 43.8 where t=8 for the year 2001
N(8) = 24.2 + 43.8
N(8) = 68.0