SOLUTION: The number of starbucks stores in the US in 2005 was 8896. In 2014, there were 11965 Starbucks stores in the US. Let y be the number of Starbucks stores in the in the year x, whe

Algebra ->  Inequalities -> SOLUTION: The number of starbucks stores in the US in 2005 was 8896. In 2014, there were 11965 Starbucks stores in the US. Let y be the number of Starbucks stores in the in the year x, whe      Log On


   

Question 1087010: The number of starbucks stores in the US in 2005 was 8896. In 2014, there were 11965 Starbucks stores in the US. Let y be the number of Starbucks stores in the in the year x, where x=0 represents the year 2005.
a) write a linear equation in slope intercept form that models the growth in number of stores in the US in terns of x. (hint: the line must pass through the points (0,8896) and (9,,119651)
b. Use this equation to predict the number of Starbucks stores in the US in the year 2020.
C. Explain what the slope for this line means int he context of the problem
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Part A)

The two points given are

A = (x1,y1) = (0,8896)
B = (x2,y2) = (9,11965)

m = Slope of line through points A and B

m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%2811965+-+8896%29%2F%289+-+0%29

m+=+%283069%29%2F%289%29

m+=+341

The slope is m+=+341.

The y intercept is b+=+8896 as this is the y value when x = 0. See point A.

So the slope intercept form y+=+mx%2Bb turns into y+=+341x%2B8896 after performing substitutions or replacements.

Answer: y+=+341x%2B8896

The graph looks like this



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Part B)

Plug x = 15 into the equation found in part A. Why this x value? Because 15 years have passed since 2005 to get to 2020 (2020-2005 = 15). Keep in mind that x = 0 represents the year 2005

y+=+341x%2B8896

y+=+341%2A15%2B8896 x has been replaced with 15

y+=+5115%2B8896

y+=+14011

We predict that there will be about 14011 stores in the year 2020 (assuming the growth rate stays the same).

Answer: 14011

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Part C)

Slope = rise/run = (change in y)/(change in x)

The change in y is the change in the number of stores

The change in x is the change in the year number

(change in y)/(change in x) = (number of stores)/(number of years) = number of stores per year

So the slope of 341 means that Starbucks is opening 341 stores per year. In other words, there are 341 new stores opening up every year.

Obviously this pace can't keep up forever.