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# Exponential Functions in Finance

Lesson 9 of 11

## Objective: SWBAT calculate mortgage payments and the balance of an installment loan using exponential functions and geometric series.

## Big Idea: The formulas for calculating loan payments look intimidating, but when we examine the structure, we see an exponential function set equal to a geometric series.

*90 minutes*

#### Warm-up

*15 min*

Students warm up by working independently to complete Benjamin Franklin Exponential Problem. This is a two page document that describes Benjamin Franklin's plan for his investment in the cities of Philadelphia and Boston. In this document, Franklin's own words describe an exponential model about how his investments will grow. Students are asked to write the mathematical function described in the text and use it to predict the value of Franklin's investment.

When students have completed this work, we discuss the exponential model and how it compares to the models they have used in the scientific problems assigned in the previous class.

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The second exponential function application packet is all about financial applications of exponential functions. Before distributing this problem set to students, I do some direct instruction in using exponential models together with geometric series in order to calculate mortgage payments [MP3]. This is a difficult concept for students (and most adults) so I want to make sure that students have the opportunity to write down notes on the process.

After taking notes, students with table partners to complete WS Financial Applications. I make solutions to the problem set available through Edmodo so that students can check their work as they go.

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#### Exit Ticket

*15 min*

Word problems that require students to combine content from more than one unit can be challenging for students, but they also report enjoying them. My students will need substantial support with loan payment problems, so I use Exit Ticket Mortgage Payments to determine what support is still needed. Evaluating these exit tickets helps me know whether to spend more time in whole-class discussions about these problems, or whether to pull individual students aside for more instruction.

#### Resources

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- LESSON 1: Properties of Exponents
- LESSON 2: Exponential Equations
- LESSON 3: Logarithms
- LESSON 4: Quiz and Graphing Exponential Functions
- LESSON 5: Multiple Representations of Exponential Functions
- LESSON 6: Quiz and Comparing Linear, Exponential Models
- LESSON 7: Drinking and Driving Activity
- LESSON 8: Exponential Models in the Sciences
- LESSON 9: Exponential Functions in Finance
- LESSON 10: Review Workshop: Exponential Functions and Logarithms
- LESSON 11: Unit Test: Logarithms and Exponential Functions