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Answer: The answer is 300 gallons.
Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.
To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ =
If a function is defined on the closed interval [a,b] and is any point in [
,
], then a Riemann Sum is defined as ∑f(
)Δ
.
For this question:
Δ =
= 1.4
Now, we have to find s(t) for each valor on the interval:
s(t) = 0.29 - t +25
s(0) = 25
s(1) = 24.29
s(2) = 24.16
s(3) = 24.61
s(4) = 25.64
s(5) = 27.25
s(6) = 29.44
s(7) = 32.21
Now, using the formula:
∑f()Δ
= 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)
∑f()Δ
= 1.4(212.6)
∑f()Δ
≅ 300
With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.