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) V (gal) 5 10 15 20 25 30 2064 1314 735 348 87 0 (a) If P is the point (15, 735) 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, 2064) (10, 1314) (20, 348) (25, 87) (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.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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)
V (gal)
5
10 15
20 25 30
2064 1314 735 348 87 0
(a) If P is the point (15, 735) 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, 2064)
(10, 1314)
(20, 348)
(25, 87)
(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.)
Transcribed Image Text: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) V (gal) 5 10 15 20 25 30 2064 1314 735 348 87 0 (a) If P is the point (15, 735) 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, 2064) (10, 1314) (20, 348) (25, 87) (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.)
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