# 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.

Dec 3, 2015

1998,$19384.50;2000,$20223;2002,$21061.50 #### Explanation: We know the following points: $\left(1996 , 18546\right)$and $\left(2004 , 21900\right)$. 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: $\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$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)