Chapter 12.1, Problem 84AYU

Environmental Control The Environmental Protection Agency (EPA) determines that Maple Lake has $250$ tons of pollutant as a result of industrial waste and that $10\%$ of the pollutant present is neutralized by solar oxidation every year. The EPA imposes new pollution control laws that result in $15$ tons of new pollutant entering the lake each year. The amount of pollutant in the lake after $n$ years is given by the recursively defined sequence

$p_0=250p_n=0.9p_{n-1}+15$.

Determine the amount of pollutant in the lake after $2$ years. That is, determine $p_2$.