How Americans Got So Jittery Name______

A cup of coffee just isn’t a cup of coffee anymore. Now it has become a social event. The Seattle based Starbucks company has grown and grown. Let’s take a look at the growth since the company’s inception and try to predict where they are going.

Visit the Starbucks website (http://www.starbucks.com/about-us/company-information) to read about the history of the company including the Company Overview Timeline. Starting with 1971, record the year and the number of stores through 2007 in the table below:

Year / Years
(beyond 1971) / Stores
1971 / 0
1987 / 16
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007

1. Are there any Starbuck’s stores in other countries? If so, can you find

where the first was opened and what year they opened?

2. Enter the years since 1971 in L1, and the Number of Stores in L2.

3. Set up Plot 1 to graph the scatter plot with L1 as the X list and L2 as

the Y list using the big square as the mark. Adjust your window

appropriately.

4. Why do you think so many points are clustered together?

5. Turn on the Transformational Graphing Application (APPS) on your

calculator. In Y= type in A(B)x. This is the basic equation of an

exponential function. Adjust the initial population, A, and the growth

factor, B, of the function y = abx, until you have a good exponential

fit for this data. Record the function. Sketch in the function on your

hand-drawn graph. WARNING: I’ve been with most of you long

enough that some of you will try to do this the quick and easy way by

completing an exponential regression. DO NOT, DO NOT, DO NOT

take the easy way out.

6. Interpret the meaning of A in your function y = abx, including the

units.

7. Interpret the meaning of the B in your function y = abx, including the

units.

8. Now use your exponential function to complete the following table:

Year / Years Since 1971 / Actual Data / Prediction based on
Exponential Model / Residual
Actual - Predicted
1990 / 19 / 84
2000
2007
2013
2050

9. How well does your function predict the number of Starbucks location in each of the years in the table above compared to the data from the Starbucks Company Time Line?

10. If Starbucks continues to grow at this same rate, how many stores do you think will be in existence in the year 2050?

Adapted from: Algebraic Thinking: NC-PIMS 6-12 Course