Pollution begins to enter a lake at time t = 0 at a rate (in gallons per hour) given by the formula ƒ(t) = 10(1 - e^-0.5t), where t is the time (in hours). At the same time, a pollution filter begins to remove the pollution at a rate g(t) = 0.4t as long as pollution remains in the lake.
(a) How much pollution is in the lake after 12 hours?
(b) Use a graphing calculator to find the time when the rate at which pollution enters the lake equals the rate at which pollution is removed.
(c) Find the amount of pollution in the lake at the time found in part (b).
(d) Use a graphing calculator to find the time when all the pollution has been removed from the lake.