# A Deeper Look at Exponential Functions

**Estimated Time:** 30 - 40 minutes

### Lesson Objectives:

- Students will apply understanding of residuals and functional behavior to determine whether an exponential function model is the best fit for a data set.
- Students will find an appropriate exponential model to fit a data set, including models that require vertical translations.
- Students will identify if the context of the situation requires discrete or continuous data.

### Resources for this lesson:

Before you begin, download your Algebra II Journal for A Deeper Look at Exponential Functions. You will be completing activities in the journal throughout this lesson.

Visit this section on each page to access information about key terms and other resources to help facilitate the lesson.

> Glossary

> Calculator Resources

> Teacher Resources: Instructional Notes

**Key Common Core State Standards:**

S.ID.6 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

- Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

**Supporting Common Core State Standards:**

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.**Standards for Mathematical Practices:**

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.