Find the upper estimate

Question

Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.Give your answer with one decimal place.

t (hr)

0

2

4

6

8

10

r(t) (gal/hr)

12.0

10.6

8.8

8.0

6.0

4.8

Answer 1

The amount of water that leaks out is the leak rate (gal/hr) times the time gone by (hrs) or, in other words, the area under the curve of this graph:

We estimate it (using rectangles, with a Riemann sum, in this case a Left Riemann sum (or upper limit because it is an over-estimate).

The area is the width of the rectangle (2) times the sum of the y-values (12.0 + 10.6 + 8.8 + 8.0 + 6.0) = (2)(45.4) = 90.8 gallons