## Reflection: Connection to Prior Knowledge Comparing Growth Models, Day 1 - Section 4: Characteristics of Exponential Growth

When I taught this lesson, I asked if anyone could give me an example of an exponential equation that we had worked with recently.  Since we'd just finished graphing quite a few of these, I was expected something like y = 3^x.  Instead, one student raised her hand and said, "Well, wouldn't that be anything with x raised to some power, like y = x^3 + 2x^2?"  This caught me completely off guard!

So, like any good teacher, I stalled for time.  "Ok," I said, "can you explain why that's an exponential equation."  She explained that it was due to the fact that it had exponents higher than degree one.  As she was speaking, I could see a number of other students nodding along.  One of them chimed in, "Yeah, wouldn't be exponential if it only has terms that have x raised to some power greater than 1?"

Somehow, we had gotten this far and they weren't familiar with the term "exponential equation"!  They though an exponential equation was just a certain kind of polynomial!  At this point, I stopped them an explained that the equations they were describing were simply polynomials.  Then I made sure to emphasize the primary distinction: in a polynomial the base varies while the exponent is constant, while in an exponential function the base is constant while the exponent varies.

Just goes to show that you really have to be careful what you take for granted!

What's an exponential equation?
Connection to Prior Knowledge: What's an exponential equation?

# Comparing Growth Models, Day 1

Unit 6: Exponents & Logarithms
Lesson 6 of 14

## Big Idea: What makes exponential growth "exponential"? A comparison with linear growth makes the answer clear.

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50 minutes

### Jacob Nazeck

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