A pond initially contains 1 000 000 gal of water and an unknown amount of an und

Question

A pond initially contains 1 000 000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.05 gram of this chemical per gallon flows into the pond at a rate of 800 gal/hr. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond.

Write a differential equation for the amount q (in grams) of chemical in the pond at any time t (in hours). Your answer should be an expression in terms of q.

Explanation / Answer

dq/dt=rate in -rate out rate in=0.05*800=40g/h rate out=q/1000000 *800=4q/5000 dq/dt=40- 4q/5000 solving gives q=50000-ce^(-4t/5000)

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