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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 tablebelow. 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 ofwater that leaked out by using five rectangles

Water leaks from a tank at the rate of rt gallons per hour The rate decreased as time passed and values of the rate at twohour time intervals are shown in the t class=

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ANSWER

72.2 gallons

EXPLANATION

We can do a graph for these rectangles to understand the problem better,

Now, we have to find the sum of the areas of these rectangles. Note that all of them have a width of 2 units, so the sum of the areas is 2 multiplied by the sum of the heights of the rectangles,

[tex]2(10.7+8.6+6.6+5.2+5)=2\cdot36.1=72.2[/tex]

Hence, the upper estimate for the total amount of water leaked out is 72.2 gallons.

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