At Harlan County Damn in Nebraska, the U.S. Bureau reports that the storage content of the reservoir decreased from 117,811 acre-feet (38.4 billon gallons of water) on Septmber 6, 2006 to 115,579 acre-feet (37.7 billion gallons of water) on October 6, 2006. Suppose that the rate of loss of water remains constant. Write an equation that relates the amount A of water, in billions of gallons, to the time t in days. Use t=1 for September 1, and so on.

1 answer

The rate of loss is
(117,811-115,579)/30 = 74.4 acre-feet per day. Aug 31 is six days earlier than Sept 6, so there would have been 6x74.4 = 446 more acre-feet then, or 118,257.

A = 118,257 - 74.4 t acre-feet

where t is measured in daya after Aug 31.
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