A factory is pollutating a lake in such a way that the rate of pollutants entering the lake at time t, in months, is given by N'(t) = 3501:\"6 where N is the total number of pounds of pollutants in the lake at time t. (a) How many pounds entered the lake in 11 months. pounds (b) A cleanup must begin after 242,000 pounds of polluntants have entered the lake. After what length of time will this occur? months