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) 1366 898 520 212 52 0
Exercise (a)
If P is the point (15, 520) 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, 1366)
(10, 898)
(20, 212)
(25, 52)
(30, 0)

(b)
Estimate the slope of the tangent line at P(15, 520) by averaging the slopes of two adjacent secant lines.

Question

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)    	1366	898	520	212	52	0
Exercise (a)
If P is the point (15, 520) 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, 1366)
(10, 898)
(20, 212)
(25, 52)
(30, 0)


(b)
Estimate the slope of the tangent line at P(15, 520) by averaging the slopes of two adjacent secant lines.

campbell_st · Answer

for part (a) find the slope of P (15, 250) and Q(5, 1366)

m = (1366 - 520)/(5 - 15) 

you can finish the calculation 

repeat the process for all the Q points... 

(b) average the slopes from P to Q(10, 898) and then P to Q(20, 212) to get an approximation for the slope of the tangent

anonymous · Answer

thank you!!