A lake contains an amount $V$ liters of water. Initially, the water contains an amount $P$ liters of a pollutant. Water is flowing into the lake at a rate of $F$ liters per second, and well mixed lake fluid is flowing out at the same rate. The ratio of pollutant to total fluid in the inflow is $r$. The amount of $p(t)$ of pollutant in the lake is

$p(t) =$ .
Hint: Set up a linear differential equation and find an integrating factor.