A tank holds 3000 gallons of water, which drains from the bottom of the tank in

Question

A tank holds 3000 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) 2094 1329 765 336 84 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 the following values. (Round your answers to one decimal place.)
Q slope
(5, 2094)
(10, 1329)
(20, 336)
(25, 84)
(30, 0)


(b) Estimate the slope of the tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal place.)

Explanation / Answer

You just need to average the slopes: You are told to find the average of the two slopes. Recall that the average of two number x and y is (x+y)/2 Slope of tangent line at t = 15 = avg of slopes of adjacent secant lines for t = 10 and t = 20 = (-80 + -53.6) / 2 = -133.6/2 = -66.8 (-80 + -53.6) / 2 = -66.8 \

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