Question

the rate of u s per capita sale of bottled water per period 2007 to 2014 could be approximate by s(t)=.25t^2-t+29
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Answer 1

Answer:

the rate of u s per capita sale of bottled water per period 2007 to 2014 could be approximate by s(t)=.25t^2-t+29

Step-by-step explanation:

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+29s(t)=0.25t2−t+29

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

\begin{gathered}t_1=2009-2007 = 2\\t_2=2013-2007 = 6\end{gathered}t1=2009−2007=2t2=2013−2007=6

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

\begin{gathered}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\end{gathered}s(t)=0.25t2−t+292∫6s(t)dt=2∫6(0.25t2−t+29)dt2∫6s(t)dt=(12t3−2t2+29t+c)∣26S(6)−S(2)=(1263−262+29∗6+c)−(1223−222+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.

Answer 2

Step-by-step explanation:

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