Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta,

Question

Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow for each lake is 100 liters per hour. Lake Alpha contains 100 thousand liters of water, and Lake Beta contains 500 thousand liters of water. A truck with 200 kilograms of Kool-Aid drink mix crashes into Lake Alpha. Assume that the water is being continually mixed perfectly by the stream.

Let x be the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. Find a formula for the incremental change in the amount of Kool-Aid, Ax, in terms of the amount of Kool-Aid in the lake x and the incremental change in time At Enter At as Deltat.

Explanation / Answer

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