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In this lesson, students will learn about applications of the exponential equation in the form **y = ca ^{x}**. Students will extract data on the farm value of potatoes over time from Statistics Canada's E-STAT database and import them into a statistical software program. Within the software program, students will model an exponential equation. By adjusting the values of the

**Contributors:** Jennifer Hall and Joel Yan, Statistics Canada

- Collect secondary data that may be represented by exponential functions
- Through investigation, determine the relationships between the graphs and the equations of exponential functions
- Through investigation, determine the basic properties of exponential functions
- Identify the effect of simple transformations
- Explain the role of
**c**,**a**, and**x**of an exponential function in the form**y = ca**^{x} - Fit the equation of an exponential function to a scatter plot using an informal process

Grades 11 and 12

Mathematics

One to two 75 minute periods

- Computers with Internet access and statistical software
- Computer projector
- E-STAT account
- E-STAT instructions
- Software instructions:
- Student worksheet
- Student worksheet – Teacher version

Exponential functions in the form **y = ca ^{x}**

Basic knowledge of E-STAT and statistical software

- Review important properties of exponential functions
**y = ca**.^{x} - Using the computer projector, demonstrate the important features of E-STAT. You may wish to use the flash presentation What's E-STAT?
- Hold a brief class discussion on the topic of potato farming and sales in Canada to assess students' prior knowledge and share information on the topic.
- Distribute the student instructions and worksheet and have students complete the lesson independently or in pairs.

Have students repeat the process of retrieving data for individual provinces or territories to see if the data follow an exponential pattern. If not, have students research reasons for this difference.

Challenge students to search on the E-STAT CANSIM database to find other time series data (among the more than 36 million time series) that can be modelled by an exponential function. They can import these data into a statistical software program and attempt to plot exponential functions to fit their data.

**Note:** Several examples are provided at Function modelling using secondary data from E-STAT.

Students will be informally assessed on their work habits and computer skills throughout this activity. They can be formally assessed via the worksheet, which can be marked using a marking scheme of the teacher's choice.