Chapter 1 Project

Modeling the Growth of a Business

In 1971, Starbucks Coffee opened its first location in Pike Place Market – Seattle’s legendary open-air farmer’s market. By 1987, the number of Starbucks stores had grown to 17 and by 1999 there were 2498 locations. As of Oct 2, 2012 there were 17,572 stores. The data in the table (obtained from Starbucks Coffee’s website summarizes the growth of this company from 1987 through 2012.

  1. Enter the data from Table 1 into your grapher or computer. (Let t=0 represent 1987.) Draw a scatter plot for the data.
  2. Refer to page 149 in the textbook. Look at the types of graphs displayed and the associated regression types. Choose the model that best matches the plotted data and the regression equation to model this data.
  3. Use the model that you just found to predict the total number of Starbucks locations for 2000 and 2001.
  4. There were 3501 Starbucks locations in 2000 and 4709 locations in 2001. Why is there such a big difference between your predicted values and the actual number of Starbucks locations?
  5. Go back and alter the data, this time including the data from both tables together. Draw a scatter plot for the entire data set.
  6. Does the scatter plot still support your original regression model choice? Explain.
  7. Recalculate the regression equation using the entire data set. Change models if needed to the one that best fits the graph.
  8. Use your new model to predict the number of Starbucks locations in 2012.
  9. The actual number of Starbucks locations as of October 2, 2012 was 17572. Was your prediction accurate? Explain.
  10. Suppose you are on the advisory board for development and planning at Starbucks. Mr. Bigbux observes all of the store data from 1987 through 2012 and he is encouraged – business is great, the number of locations is increasing at an exponential rate every year, and he is looking forward to opening thousands of new stores in the future. When you point out how the growth has slowed over the most recent years, Mr. Bigbux just shrugs and blames it on the slow economy. Surely business will pick up when things settle back down, and by 2020 there can be over 200,000 stores according to the exponential growth model. Create a poster, pamphlet, business memo, power point presentation, media file, or some other visual way of conveying to Mr. Bigbux that 200,000 stores will not be possible. Be sure to mathematically support your argument.