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Question 409495: I need help figuring out my homework problem. I am lost and need steps to help me complete.
According to surveys conducted from 2000 to 2010, Fun Pop's percentage of soft drink market declined from 14.2% in 2002 to 13.4% in 2007. If the percentage declined linearly during this time, then do the following
1. Find the linear equation that can be used to predict the Fun Pop's percentage of soft drink market, y, based on the year, x.
2. What is the slope of the linear equation and its interpretation
3. Find the x-intercept and interpret its meaning
4. Predict Fun Pop's percentage of soft drink market in 2014.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! According to surveys conducted from 2000 to 2010, Fun Pop's percentage of soft drink market declined from 14.2% in 2002 to 13.4% in 2007.
If the percentage declined linearly during this time, then do the following
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You have two points: (2002,14.2) and (2007,13.4)
1. Find the linear equation that can be used to predict the Fun Pop's percentage of soft drink market, y, based on the year, x.
slope = (13.4-14.2)/(7-2) = -0.8/5 = -0.16
Form: y = mx + b
13.4 = (-0.16)*7+b
b = 14.52
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Percent = -0.16(year after 2000)+14.52
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2. What is the slope of the linear equation and its interpretation
slope = -0.16
The Fun Pop's % of the market decreases 0.16% each year after 2000.
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3. Find the x-intercept and interpret its meaning
Percent intercept: P = 14.52
In 2000 the % of market share was 14.52.
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Year intercept = ?
Solve -0.16x+14.52 = 0
-0.16x = -14.52
x = 90.75
In the year 2091 the % market share will be zero.
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4. Predict Fun Pop's percentage of soft drink market in 2014.
P(14) = -0.16(14)+14.52
P(14) = 12.28%
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Cheers,
Stan H.
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