We want to know how many years it would take for the pollution in a lake to reach 5% of its current level, assuming no pollution flows in. Make some simplifying assumptions to estimate this. (Hint: first build a model for the rate of change of the total pollution in the lake). Find this time for Lake Erie, Lake Michigan, Lake Superior, and the Great Salt Lake where their volumes, V (in cubic meters) and outflow of water r (cubic meters per day) are given in the following table

Lake, Volume (V), Outflow of water (r)

Erie, 458 10^9, 479 10^6

Michgan, 4,871 10^9, 433 10^6

Superior, 12,221 10^9, 178 10^6

Great Salt, 18.9 10^9, 0

Clearly state your simplifying assumptions and comment on sources of error