Answer: A pond containing 1,000,000 gal of water is initially free of a certain

Chapter 1, Problem 18

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A pond containing 1,000,000 gal of water is initially free of a certain undesirable chemical (see of Section 1.1). Water containing 0.01 g/gal of the chemical flows into the pond at a rate of 300 gal/h, and water also flows out of the pond at the same rate. Assume that the chemical is uniformly distributed throughout the pond. (a) Let Q(t) be the amount of the chemical in the pond at time t. Write down an initial value problem for Q(t). (b) Solve the problem in part (a) for Q(t). How much chemical is in the pond after 1 year? (c) At the end of 1 year the source of the chemical in the pond is removed; thereafter pure water flows into the pond, and the mixture flows out at the same rate as before. Write down the initial value problem that describes this new situation. (d) Solve the initial value problem in part (c). How much chemical remains in the pond after 1 additional year (2 years from the beginning of the problem)? (e) How long does it take for Q(t) to be reduced to 10 g? (f) Plot Q(t) versus t for 3 years.