Chapter 13.FOM, Problem 4P

Pollution A chemical plant discharges $2400\text{tons}$ of pollutants every year into an adjacent lake. Through natural runoff, $70\%$ of the pollutants contained in the lake at the beginning of the year are expelled by the end of the year.

(a) Explain why the following sequence models the amount $A_n$ of the pollutant in the lake at the end of the $n\text{th}\text{year}$ that the plant is operating.

$A_n=0.30a_{n-1}+2400$

(b) Find the first five terms of the sequence $A_n$.

(c) Find a formula for $A_n$.

(d) How much of the pollutant remains in the lake after $6\text{years}$? How much will remain after the plant has been operating a long time?

(e) Verify your answer to part (d) by graphing $A_n$ with a graphing calculator for $n=1$ to $n=20$.