A lake has various streams flowing into it and flowing out of it, the total rates of influx and efflux being equal. For a long time, the streams flowing into the lake were polluted, and pollu- tion in the lake built up to an undesirable level. However, as a result of conservation efforts, the sources of pollution in the streams were eliminated, and now only pure water flows into the lake. If the volume of the lake is V km', if the rate of influx and efflux is r km/year. and if the pollutants are always uniformly distributed throughout the lake, obtain formulas for the time it will take for the pollution in the lake to be reduced (a) to one-half its level at the time of the clean-up and (b) to one-tenth its level at the time of the clean-up. Determine numerical valucs for these times for Lake Erie and Lake Ontario, given the following data: V 175 km³/yr 209 km³/yr Lake Eric 460 km3 Lake Ontario 1,600 km3