A stream feeds into a lake at a rate of 1000 m³/day. The stream is polluted with a toxin whose concentration is 5 g/m³. Assume that the lake has volume 10⁶ m³ and that water flows out of the lake at the same rate of 1000 m³/day.
(a) Set up a differential equation for the concentration c(t) of toxin in the lake and solve for c(t), assuming that c(0) = 0. Find the differential equation for the quantity of toxin y(t), and observe that c(t) = y(t)/10⁶.
(b) What is the limiting concentration for large t?