Use midpoint formula to estimate sales

Question

A soda company had sales of $19,574 million in 2002 and $35,113 million in 2010. Use the Midpoint Formula to estimate the sales in 2006. Assume that the sales followed a linear pattern.

Answer 1

The Midpoint Formula is:
 
     ( (x₁+x₂)/2, (y₁+y₂)/2 )
 
The given points are:
     P₁:   (2002,$19.574 million)
     P₂:   (2010, $35.113 million)
Note:  the sales (dependent variable) are a function of the year (the independent variable)
 
Using the Midpoint Formula, the Midpoint between P₁ and P₂ is:
     ( (2002+2010)/2, ($19,574 million + $35,113 million)/2 )
      (  2006, $27.3435 million )
 
Fortunately, the problem asks for year=2006, the middle year of the problem.  Otherwise we would do linear estimation as other tutors have suggested.
 
Note:  We cannot assume zeros, but the dollar amount in 2006 is approximately $27,343,500.00.

Answer 2

Hello Cheree,

 

Assuming that the slope is the same, estimated sales x in any year Y can be found from the following general equation applicable to any point between Y2002 and Y2010:

(35,113m - 19,574m) / (2010 - 2002) = (x - 19,574m ) / (Y - 2002)

 

Pertinent to this case:

 

(35,113m - 19,574m) / (2010 - 2002) = (x - 19,574m ) / (2006 - 2002)

Next, simplify and solve linear equation for x (you can use online Linear Equation Solver: http://examn8.com/LinearEquations.aspx):

x - 19,574m = 7,769.5m
x= $27,343.50m

In a simplified way applicable just to a Midpoint (per definition), the answer can be calculated as:
X= $19,574m + 1/2($35,113m - $19,574m)

 

Hope this will help.

Answer 3

Note that (2002+2010)/2 = 2006, so if the sales grows linearly, we are looking for the midpoint between the years given.

 

The salary predicted by the midpoint formula is

 

$ (19,574 + 35,113) / 2 = $ 54,687 / 2 = $27,343.50