Question

please show work because i'm confused. this is a calculus 2 class

1. Water flows into and out of a storage tank. A graph of the rate of change, r), of the volume of water in the tank (in liters per day) is shown below. Suppose the amount of water in the tank at time t=0 is 25,000 liters. Use M, to estimate the amount of water in the tank four days later. 2000 1000 0 2 41 -1000

Answer 1

M4 represents the mid-point rule estimate with four intervals

Delta x = (b-a)/n = (4-0)/4 = 1

So, the intervals will be [0,1],[1,2],[2,3] and [3,4], the mid-points will be 0.5,1.5,2.5 and 3.5

From the graph,

r(0.5) = 1500

r(1.5) = 1750

r(2.5) = 1000

r(3.5) = -500

M4 change estimate = Delta x(r(0.5) + r(1.5) + r(2.5) + r(3.5)) = 1(1500+1750+1000-500) = 3750

Amount of water in tank 4 days later = Initial water level + Change = 25000 + 3750 = 28750 liters

Note - Post any doubts/queries in comments section.