Question

Year	years since 1971	number of new locations
1971	0	1
1987	16	17
1988	17	33
1989	18	55
1990	19	84
1991	20	116
1992	21	165
1993	22	272
1994	23	425
1995	24	677
1996	25	1015
1997	26	1412
1998	27	1886
1999	28	2498
2000	29	3501
2001	30	4709
2002	31	5886
2003	32	7225
2004	33	8569
2005	34	10241
2006	35	12440
2007	36	15011
2008	37	16680
2009	38	16635
2010	39	16858
2011	40	17003
2012	41	18066
2013	42	19767
2014	43	21366
2015	44	22519

And now here we are…a Starbucks on nearly every corner. Even Homer Simpson had something to say about this in a recent episode! This is where I need your help. I would like you to perform a thorough analysis of the data involving the number of Starbucks locations. Our investors are interested to know about the rate of growth as well as to understand issues related to forecasting the number of Starbucks locations in the future. And specifically, we are wondering when the number of stores will reach 37,000 locations. You see, there are currently 37,000 McDonald’s restaurants worldwide, and we have set a goal to reach that number by the year 2020. Do you think we can do it?

1. identify the initial value and the growth rate of your exponential model and explain what they mean in context of Starbucks Stores. Put your explanations in a text box.
2. How well does the exponential function compare to the data from the Starbucks Company Time Line? Answer in a short paragraph in a text box.
3. Use your exponential model to predict when Starbucks will match McDonald’s for the number of locations.

Answer 1

Compute exponential trendline using Google Sheets or MS-Excel as follows:

the fitted exponential model is: y= 121.e^0.124x , where y- no. of Starbucks locations and x- no. of years since 1971.

Here,

initial value = 121 and

growth constant= 0.124

This means the frequency (number of times per year) of the number of Starbucks locations growing by a factor e is 0.124, where initial number of locations is 121.

R²=0.911. So 91.1% of variation in number of locations is explained by the exponential model where "No. of Years since 1971" is the explanatory variable. We can say that the exponential function compared very well to the Starbucks Company Time Line.

Now putting y=37000 in fitted equation, we get x=46.15. So we can predict that the number of Starbucks locations will match McDonald's in the year (1971+46)= 2017.