A chemical plant is adding pollution to a lake at the rate of 35?3 tons per year, where t is the number of years that the plant has been in operation.(a) Find a formula for the total amount of pollution that will enter the lake in the first t years of the plant's operation. [Hint: Evaluate C so that no pollution has been added at time t = 0.]P(t) =(b) Use the formula that you found in part (a) to find how much pollution (in tons) will enter the lake in the first 4 years of the plant's operation. (Round your answer to the nearest whole number.)P(4) = tons(c) If all life in the lake will cease when 200 tons of pollution have entered the lake, will the lake "live" beyond 4 years?