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Levart [38]
3 years ago
6

The rate of U.S. per capita sales of bottled water for the period 2007–2014 could be approximated by s(t) = 0.25t2 ? t + 29 gall

ons per year (0 ? t ? 7), where t is time in years since the start of 2007.† Use a definite integral to estimate the total U.S. per capita sales of bottled water from the start of 2009 to the start of 2013. (Round your answer to the nearest gallon.)
Mathematics
1 answer:
julsineya [31]3 years ago
6 0

Answer:

117 gallons

Step-by-step explanation:

The expression that describes the rate of U.S. per capita sales of bottled water for the period 2007–2014 is:

s(t) = 0.25t^2-t+29

Since t=0 at 2007. At 2009 and 2013, t is:

t_1=2009-2007 = 2\\t_2=2013-2007 = 6

The definite integral of the expression from t=2 to t=6 is:

s(t) = 0.25t^2-t+29\\\int\limits^6_2 {s(t)} \, dt= \int\limits^6_2 {(0.25t^2-t+29)} \, dt\\\int\limits^6_2 {s(t)} \,dt= (\frac{t^3}{12} -\frac{t^2}{2}+29t +c)|^6_2 \\S(6) -S(2) = (\frac{6^3}{12} -\frac{6^2}{2}+29*6 +c) - (\frac{2^3}{12} -\frac{2^2}{2}+29*2 +c)\\S(6) -S(2) = 117.333\ gallons

Rounded to the nearest gallon, the estimated total U.S. per capita sales of bottled water from the start of 2009 to the start of 2013 is 117 gallons.

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