A tank holds 1000 gallons of water which drains from the bot

A tank 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.

(a) If P is the point (15, 245) 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.)

(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.)

Solution

a)

P(15,245)

i) (5,680) : Slope = (680-245)/(5 - 15) = -43.5

ii) (10,433) : Slope = (433-245)/(10 - 15) = -37.6

iii) (20,111) : Slope = (111-245)/(20 - 15) = -26.8

iv) (25,25) : Slope = (25-245)/(25 - 15) = -22

v) (30,0) : Slope = (0-245)/(30 - 15) = -16.3

b)

(680 - 1000) / 5 = -64
(433 - 680) / 5 = -49.4
(245 - 433) / 5 = -37.6
(111 - 245) / 5 = -26.8
(25 - 111) / 5 = -17.2
(0 - 25) / 5 = -5

Pairwise, the averages are:
roughly -56.7
roughly -43.5
roughly -33.2
roughly -22
roughly -11.1