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  3. 12200 4 consider a lake of constant volume 12200 k

12200 4 Consider a lake of constant volume 12200 km3 which at time contains an...

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12200 4 Consider a lake of constant volume 12200 km3 which at time contains an amount y t tons of y 1 pollutant evenly distributed throughout the lake with a concentration tons km Assume that fresh water enters the lake at a rate of 67 1 km yr and that water leaves the lake at the same rate Suppose that pollutants are added directly to the lake at a constant rate of 550 tons yr Among the many simplifying assumptions that must be made to model such a complicated real world process is that the pollutants coming into the lake are instantaneously evenly distributed throughout the lake A Write a differential equation for y t B Solve the differential equation for initial condition y 0 200000 to get an expression for y t Use your solution y t to describe in practical terms what happens to the amount of pollutants in the lake as goes from 0 to infinity

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