According to surveys conducted from 2000 to 2010 , Fun Pop\'s percentage of soft

Question

According to surveys conducted from 2000 to 2010 , Fun Pop's percentage of soft drink market declined from 10.8 % in 2000 to 8.9 % in 2006. If the percentage declined linearly during this time, then to do the following :

A) Find the liner equation that can be used to predict Fun Pop's percentage of the soft drink market y, based on the year , X . show how you arrived at your answer

B) What is the slope of the linear equation and give it interpretation

C) Find the x- intercept and interpret its meaning

D) Predict Fun Pop's percentage of the soft drink market in 2014 , show how you arrived at your prediction

E) What assumption are you making for the predicted value in part (d)

Explanation / Answer

A)
First we need to calculate the slope. The rise over run which is the change in y over the change in x
We denote x=0 corresponding to the first year, 2000.

m = (8.9-10.8)/(6-0)
m = -.316666666

y-10.8 = -.316666666x
y = -.316666666x+10.8

B)
m = -.316666666

C)
0 = -.316666666x+10.8
x = 34.1

The year 2034 which is the year that there will be a 0% soft drink market.

D)

Using our linear approximation formula

y = -.316666666x+10.8

let x =14

y = -.316666666*14+10.8

y = 6.37%

E) We are assuming that the trend from 2000 to 2010 remains linear till the year 2014 and extrapolating that data.

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