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A tank holds 2000 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) 1392 870 480 214 58 Exercise (a) If P is the point (15, 480) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with the following values. Q (5,1392) (10,870) (20,214) (25,58) (30,0) Step 1 Slopes of secant lines passing through P(15, 480) and Q(t, V(t)) can be calculated using msec - V(t) 480 t 15 We begin by calculating the slope when t = 5. V(5) 480 msec = 5 15 - 480 = = (rounded to the nearest tenth) Exercise (b) Estimate the slope of the tangent line at P(15, 480) by averaging the slopes of two adjacent secant lines. Step 1 Looking at the table, the t-values adjacent to t = 15 are t = (smaller value) t = (larger value).

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