A lake containing $\displaystyle {1.6}\times{10}^{{9}}$ liters of water is polluted with 3 mg/L of arsenic. A freshwater stream feeds the lake at a rate of $\displaystyle {5.2}\times{10}^{{7}}$ liters per day, while another stream drains the lake at the same rate. Pretending that there was a large blender keeping the lake well mixed:

a) Set up a differential equation to describe the milligrams of arsenic, $\displaystyle {y}{\left({t}\right)}$, in the lake after $\displaystyle {t}$ days.

$\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}$ = Preview Question 6 Part 1 of 3  

b) Solve it.

$\displaystyle {y}{\left({t}\right)}$ = Preview Question 6 Part 2 of 3  

c) If 0.01 mg/L of arsenic is considered safe by the EPA, how long will it be before the lake is safe again?

Preview Question 6 Part 3 of 3   days