Question
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
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) | 5 | 10 | 15 | 20 | 25 | 30 |
---|---|---|---|---|---|---|
V (gal) | 2,076 | 1,302 | 765 | 357 | 87 | 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, 2,076) | |
(10, 1,302) | |
(20, 357) | |
(25, 87) | |
(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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