Question

A soda company had sales of $19,550 million in 2002 and $35,145 million in 2010. Use the midpoint formula to estimate the sales in 2006. Assume that the sales followed a linear pattern.

Answer 1

We can draw a graph where the x-axis represents the years, and the y-axis represents the sales.

So the points are (2002, 19550) and (2010, 35145), where the second coordinate represents the sales made in the year written in the first coordinate.

and the line drawn through these 2 points represents the sales in the other years.

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Given any 2 point P(m,n) and Q(k,l),

the coordinates of the midpoint of the line segment PQ are given by the formula:


`M_(PQ)=( (m+k)/(2) , (n+l)/(2))`,

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Thus, the midpoint of points (2002, 19550) and (2010, 35145) is given by


`( (2002+2010)/(2), (19,550+35,145)/(2))= (2006, 27347.5)`


Thus, the sales in 2006 are approximately $ 27,347.5