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A tank holds 2,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show
A tank holds 2,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.
t (min) | 5 | 10 | 15 | 20 | 25 | 30 |
---|---|---|---|---|---|---|
V (gal) | 1,398 | 880 | 510 | 212 | 58 | 0 |
(a)If P is the point (15, 510) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with
t = 5,
10, 20, 25, and 30.(b)Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P.
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