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?
Loading resource...

Comparing Growth Models, Day 1

Unit 6: Exponents & Logarithms
Lesson 6 of 14

Objective: SWBAT compare and contrast linear and exponential growth. SWBAT describe a situation in which each type of model is appropriate.

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

  Print Lesson
1 teacher likes this lesson
calc exponential
Similar Lessons
How Much Will College Cost in the Future?
12th Grade Math » Exponential and Logarithmic Functions
Big Idea: Use real data to estimate college costs for the next generation.
Troy, MI
Environment: Suburban
Tim  Marley
Leap of Faith!
Algebra I » Bridge to 10th Grade
Big Idea: Students will find a linear relationship between the number of rubber bands and height.
Washington, DC
Environment: Urban
Noelani Davis
Rabbit Run -- Day 2 of 2
Algebra I » Quadratics!
Big Idea: Students look for and express regularity in repeated reasoning (MP8) as they generalize a formula.
Boston, MA
Environment: Urban
Amanda Hathaway
Something went wrong. See details for more info
Nothing to upload