SWBAT write exponential equations.
SWBAT use the properties of exponents to interpret expressions for exponential functions

Build your understanding of what that exponential function actually represents by rewriting them to reveal key features.

5 minutes

I begin this class with the same equation I used for Power to the Mathematician, to help my students make the connection between earlier lessons and what we're doing today. I discuss this further in my video.

* P(e^(rt)) *

I ask my students to talk with their right-shoulder partner about what the key features of function are and what each represents in terms of the $5000 investment problem.** (MP7) **After a few minutes or when the talk dies down I randomly select students to share what they discussed. Usually at least a few teams talked about the fact the the curve is positive, becomes very steep and never crosses the x-axis. If not, I ask leading questions like "Is this function increasing or decreasing as you move from negative to positive along the x or y axis?" I remind my students that an exponential equation that curves up and to the right as this one does is considered a "growth" curve and one that curves in the opposite direction is called a "decay" curve. These should not be new terms, but I try not to make assumptions about my students' mathematical vocabulary!

35 minutes

I tell my students that for this activity they will be working with their left-shoulder partner to rewrite exponential functions in order to be able to use their properties to interpret what key features are and what they represent. I distribute the Exponential Functions worksheet, ask if there are any questions, then tell my students they have about 25 minutes to complete this assignment and be ready to present their work to the class. **(MP1, MP2)** Some students will struggle with how to rewrite these functions because they aren't comfortable moving between logarithmic and exponential equations. For those students I ask questions like "How could you rewrite this equation so that the t isn't an exponent?" If that doesn't help I may remind them of how to rewrite an exponential function as a log function, using a simple example like y=10^x. When everyone is done or after about 25 minutes I randomly select teams to post their work on the board, with the first team showing problem #1, the second team problem #2, and so on. I can have at least two or three problems posted at the same time which takes some of the pressure off the students posting. When the board is full, I ask the class to critique each problem for accuracy and completeness. **(MP3)** We repeat the process for the last 2-3 problems so that all of the problems have been posted.

10 minutes

Before I close this lesson I tell my students they will be summarizing our class discussion in their own words in their notes for future reference. We then have a class discussion of the key features of exponential functions and how rewriting can give different insights into those features, then students complete their summaries.** **