A lank holds 1000 gallons of water, which drains from the bottom of the tank in

Question

A lank holds 1000 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. If P is the point (15,250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with f = (a) 5, (b) 10, (c) 20, (d) 25, and (c) 30. Round your answers to the nearest tenth. Estimate the slope of the tangent line at P by averaging the slopes of two secant lines using the values of t closest to P. NOTE: It turns out that the slope of the tangent line is approximately -33.3 (Can you verify that?). gal/min gal/min gal/min gal/min gal/min gal/min

Explanation / Answer

There are 6 secant lines: (694 - 1000) / 5 = -306/5 = -61.2 (444 - 694) / 5 = -250/5 = -50 (250 - 444) / 5 = -194/5 = -38.8 (111 - 250) / 5 = -139/5 = -27.8 (28 - 111) / 5 = -83/5 = -16.6 (0 - 28) / 5 = -28 / 5 = -5.6 The average of all of them is -1000/30 = -33.3 Pairwise, the averages are: roughly -55 roughly -44 roughly -33 roughly -22 roughly -11

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