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# Writing Exponential Functions to Solve Problems

Lesson 20 of 26

## Objective: Students will be able to write exponential functions and equations to solve problems more efficiently. Students will be able to solve these equations using data tables, guess-and-check or other methods.

#### Sharing and Closing

*10 min*

I ask all students to think about these questions, and to write their initial thoughts.

The questions are deliberately open-ended and broad so that all students can answer the same questions, even though they have been working on different problems. The goal for all students is to explain how to use exponential functions to solve the problems they were working on. The challenge for most students will be to explain how this process is different depending upon the different information that is given. Students may struggle to articulate this, so this is a good example of a time to focus on **MP6**, and ask students to explain their thinking as precisely as possible.

Additionally, the closing asks students to assess their level of understanding. Hopefully, students will identify that they don't really have a good way to "work backwards" with these exponential functions. If some students bring up logarithms, that is great, but don't tell them that they are right. Ask them why they think logarithms might apply, or how to use them. The goal of the closing is to surface some of these questions. This is one important aspect of **MP1**, for students to identify their strengths and weaknesses.

#### Resources

*expand content*

- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Bunnies and Exponential Growth
- LESSON 2: More Bunnies and Exponential Growth
- LESSON 3: Candy Bars and Exponential Decay
- LESSON 4: Bunnies and Exponential Equations
- LESSON 5: Graphing Bunnies
- LESSON 6: Exponential Data Tables
- LESSON 7: Fitting Exponential Functions Given Two Points
- LESSON 8: Matching Exponential Graphs to Equations
- LESSON 9: Exponential Functions Review
- LESSON 10: Exponential Functions Portfolio and Summative Assessment
- LESSON 11: Exponential Functions and Approach Statements
- LESSON 12: Graphing Exponential Functions
- LESSON 13: Matching Graphs of Exponential Functions to their Equations
- LESSON 14: Exponential Function Designs
- LESSON 15: Graph Exponential Functions Review
- LESSON 16: Graph Exponential Functions Summative Assessment and Portfolio
- LESSON 17: Bouncy Ball Investigation
- LESSON 18: Percent Change: Growth and Decay
- LESSON 19: More Percent Changes and Exponential Functions
- LESSON 20: Writing Exponential Functions to Solve Problems
- LESSON 21: Different Time Intervals and Exponential Functions
- LESSON 22: Compound Interest
- LESSON 23: Compound Interest Formula
- LESSON 24: Continuously Compounded Interest
- LESSON 25: Applications of Exponential Functions Review
- LESSON 26: Applications of Exponential Functions Summative Assessment