# Growth of Starbucks

#### 1 Hook

Use the Kahoot or Poll Everywhere site to gather information related to students' prior knowledge of exponential equations. Please feel free to change these questions to meet your educational needs. In addition, you may want to consider showing graphs as well.

**Question 1:** Which of the following is an exponential function?

- f(x) = 2x + 4

**Question 2: **Which of the following equations is showing exponential growth?

- f(x) = 2x + 4
- f(x) = 0.3x^3
- f(x) = 2*1.2^x
- f(x) = 3*0.4^x

**Question 3:** Which of the following equations is showing expoential decay?

- f(x) = 2x + 4
- f(x) = 0.3x^3
- f(x) = 2*1.2^x
- f(x) = 3*0.4^x

Student will access Kahoot.it and type in the pin number and your first name. You'll need to wait for direction from your teacher.

#### 2 Direct Instruction/Independent Work (Gather the data)

Ask the students for the definition of actuary, if they don't know the answer direct them to dictionary.com. Once they find the definition inform the students that they will be actuaries for Starbucks to exam the growth of the Starbucks corporation since 1971.

**Essential questions that will be answered:**

- How fast is Starbucks growing its stores and is it growing too fast? (This might be a more difficult question to answer for now).
- How much has Starbucks grown since 1971? (Offer suggestions such has percent increase or amount of additional stores.)

**Gather the data:**

*(You could print out this document)*

Students should access the following document by clicking on the link below and record the year and number of stores found in Desmos or Google Sheets or MS Excel. I also recommend the following iPhone or iPad App. It is not currently reviewed on Graphite, but I found it to be a great app for graphing functions. https://itunes.apple.com/us/app/free-graphing-calculator/id378009553?mt=8

Students should record 1971 as an x value of 1 and increase by one for each year. The y value would be the number of stores.

http://globalassets.starbucks.com/assets/5deaa36b7f454011a8597d271f552106.pdf

*Teacher note: Keep in mind the goal will be to graph the data and determine an exponential regression equation to determine growth rate. So chose the application that will best serve this purpose.*

Using the document provided by your teacher or found at the following site http://globalassets.starbucks.com/assets/5deaa36b7f454011a8597d271f552106.pdf record the number of Starbuck stores for the years shown.

The x value of your data is the number of years stores have been opened. (i.e. 1971 would be x = 1, 1972 would be x = 2, etc.). Record the number of stores as the y value that corresponds to the year. Use Desmos, Google Sheets, or MS Excel to record the data. If you have an iPhone or iPad you may want to consider purchasing the app found by accessing this link.

After you have gathered the data, think about the following questions prior to graphing the data. You don't have to have answer at this time in the lesson.

- How fast is Starbucks growing its stores and is it growing too fast?
- How much has Starbucks grown since 1971?

#### 3 Independent Work--Graph the Data

For this step students should graph the data using Desmos or Google Drive. You may even chose MS Excel to graph the data using a scatter plot.

Questions to ask the class:

- What type of data appears to be displayed in the graph?
- What type of function do we need to model this data?
- How can we calculate the regression equation?

Graph the data with the technology tool that you have chosen to record the data. (Desmos, Sheets, or Excel)

Once you have graphed the data answer the following questions:

- What type of data appears to be displayed in the graph?
- What type of function do we need to model this data?
- How can we calculate the regression equation?

#### 4 Independent Work--Examining the data

For this part of the lesson, Desmos does not calculate a regression equation. If you use the Apple app mentioned above you will be able to have the students create an exponential regression equation. If this isn't possible then have students select two points and use the equation y = ab^x to find a value for a and b using a system of equations. You may want to have students try several points and graph these equations using Desmos to see which one best fits the graph. This would also be a good time to discuss whether this is the best model for this type of data.

**(Advanced students): You may want to use the information on the site below to challenge students to complete the task with paper and pencil.**

http://www.zweigmedia.com/RealWorld/calctopic1/regression.html

Using the equation y = ab^x, chose two points and determine the equation of best fit. This will require you to a system of equations.

Calculate an equation that best fits the data. You may want to consider manipulating the *a* and *b* values to create an equation that is close to "best fitting" the data.

How does your graph "fit" the data?

Is this the best model for this data? Why or why not?

#### 5 Wrap up/Closure

Using Socrative, create an exit ticket that has students list the equation they have found and describe how well it fits the data. You may even want them to post the graph of the data. Also some questions to readdress.

- Is this the best model for this data?
- Who would benefit from the data?
- At what rate are the stores growing?
- Do you think Starbucks will continue to grow at this rate?

(optional activitiy) If time would allow you may want students to create a report to submit to you (VP of Marketing) analyizing the growth of the stores, possible conjectures about the future, and whether this trend in growth will continue.

Your teacher will direct you to an exit ticket using Socrative to post your findings (equation, graph, etc.)

(optional activity)Write a brief summary of your findings (equation of best fit, growth rate, etc), which should include the data, graph of the data, and regression equation. Some questions to consider for the report.

- What does this data tell us about the growth of Starbuck stores
- Will this growth continue at its current rate or does it appear to be slowing down? (provide data to support your conclusion)
- How could your analysis help the Starbucks corportation.

#### 6 Extension Opportunities

You may want students to examine parts of the graph.

**For example **

- What happened during the first 15 years?
- Is the data from the first year to year 36 more aligned to an exponential model?
- What is happening after year 36? And, what conjectures can we make about this time period?
- You may want students to research other ways to analyze this type of data.
- While number of stores and growth of stores is important, what other data can or should be used to determine the overall health of the Starbucks corporation?