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Thelake near Grassy Narrows is contaminated with mercury from an oldpaper mill, which has been shut down for many years. Some of thepeople who eat fish from the lake are showing signs of mercurypoisoning. Mercury is still leaking into the lake but no one knowsthe exact location of the leak. Marginal damages per year are givenby MD = 0.02E (t = 0, …) and emissions are E = 4000. The cost tolocate the leak and clean up the lake is $2 million (t = 0).a) If r = 2% and you use a 100 year time frame (t = 0, …, 99)calculate the NPV to clean the lake.b) If r = 8% and you use a 100 year time frame (t = 0, …, 99)calculate the NPV to clean the lake.c) If r = 2% and you use a 50 year time frame (t = 0, …, 49)calculate the NPV to clean the lake.d) If r = 8% and you use a 50 year time frame (t = 0, …, 49)calculate the NPV to clean the lake. e) Why are the present valuesfor the damages using the 50 year time frame (half the time) nothalf of the present values using the 100 year time frame?