The Coca-Cola Company had sales of $18,546 million in 1996 and $21,900 million in 2004. How would I use the Midpoint formula to estimate the sales in 1998, 2000, and 2002? Assume that the sales follow a linear pattern.

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Answer 1 · 2015-12-03T03:06:52

#1998,$19384.50;2000,$20223;2002,$21061.50#

We know the following points: #(1996,18546)# and #(2004,21900)#.

If we find the midpoint of these points, it will be at the assumed point for the year #2000#.

The midpoint formula is as follows: #((x_1+x_2)/2,(y_1+y_2)/2)#

This can be restated as simply finding the average of the #x#-coordinates and the average of the #y#-coordinates.

The midpoint of the two points we've already established:

#((1996+2004)/2,(18546+21900)/2)rarrcolor(blue)((2000,20223)#

Thus, the estimated sales in #2000# would be #$20223#.

We can use the same logic to find #1998# and #2002#:

#1998# is the midpoint of the #1996# and #2000# points.

#((1996+2000)/2,(18546+20223)/2)rarrcolor(blue)((1998,19384.5)#

#2002# is the midpoint of the #2000# and #2004# points.

#((2000+2004)/2,(20223+21900)/2)rarrcolor(blue)((2002,21061.5)#