One of the earliest pollution problems brought to the attention of the Environmental

Chapter 5, Problem 45

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One of the earliest pollution problems brought to the attention of the Environmental Protection Agency (EPA) was the case of Sioux Lake in eastern South Dakota. For years a small paper plant located nearby had been discharging waste containing carbon tetrachloride (CCl4) into the waters of the lake. At the time the EPA learned of the situation, the chemical was entering at a rate of 16 cubic yards/year. The agency immediately ordered the installation of filters designed to slow (and eventually stop) the flow of CCl4 from the mill. Implementation of this program took exactly three years, during which the flow of pollutant was steady at 16 cubic yards/year. Once the filters were installed, the flow declined. Fromthe time the filters were installed until the time the flow stopped, the rate of flow was well approximated by Rate (in cubic yards/year) = t2 14t + 49, where t is time measured in years since the EPA learned of the situation (thus, t 3). (a) Draw a graph showing the rate of CCl4 flow into the lake as a function of time, beginning at the time the EPA first learned of the situation. 280 Chapter Five ACCUMULATED CHANGE: THE DEFINITE INTEGRAL (b) How many years elapsed between the time the EPA learned of the situation and the time the pollution flow stopped entirely? (c) How much CCl4 entered the waters during the time shown in the graph in part (a)?

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