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A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table
A tank holds 3,000 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) V (gal) 5 10 15 20 25 30 2,058 1,320 765 336 81 0 (a) If P is the point (15, 765) 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. (Round your answers to one decimal place.) Q Slope (5, 2,058) (10, 1,320) (20, 336) (25, 81) (30,0) (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. (Round your answer to one decimal place.)
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