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# Fitting Exponential Functions Given Two Points

Lesson 7 of 26

## Objective: Students will be able to develop a method to find an exponential function that fits two given points.

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#### Closing

*10 min*

As always, the exit ticket is important to help all students focus on some of the big ideas of the lesson.

To answer the first question, it is great for students to articulate the fact that roots help us solve equations involving exponents when the base is the unknown. In a later unit, students will solve exponential equations using logarithms when the exponent is unknown, so it is important for them to articulate this idea now.

The second question is a great opportunity for students who have not used equation or who have not used both sets of equations to look at a different method. Both equations would enable a student to find the multiplier. An interesting higher level discussion is to talk about the pros and cons of each method. The first method is faster in that there is only one equation, but it doesn’t give any information about the starting value. The second method takes a little longer because the equations need to be manipulated, but then it is easy to use the original equations to find the starting value.

Hopefully, students are able to say that the function is decreasing if the outputs are getting smaller as the x-values get bigger, but they may need some coaching about how to actually write this sentence. This is a good time to give the sentence frame, “A function is ______________ if as ___________, _____________.” Though it seems very simple, it can help them organize their thoughts articulately.

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- 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