Introduction:

This is a set of guiding questions for creating your own lesson plan on how to identify, construct, and analyze simple exponential functions.

Common Core State Standards:

F.BF.3, F.IF.4, F.IF.5, F.IF.7

Learning Objectives:

To identify, construct, and analyze simple exponential functions.

Guiding Questions:

In the story about the legendary origins of chess in India, the following problem is posed:

If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the end?

Can we graph the data? How?
Is that a function?
What is a function? What is a relation?
What would happen if instead of doubling the amount of grains of wheat we would triple it? Quadruple it?
Why do all of those graphs intersect at x = 0?
What would happen if we had a giant wheat of grain we could cut in half from square to square? How small would the last piece be?
Can we graph that? How does it differ from the previous graphs?
What happens if we consider negative values of x?
What happens if the base is 1? What if it is 0?
Why can’t the base be negative?

Notes for Teachers:

You may want to graph those functions using an online graphing calculator, like Desmos. You can graph several graphs with different colors on the same coordinate axis.
If you do so, you may want to restrict the domain of the exponential functions to non-negative real numbers. Alternatively, you may show only the first quadrant and show the entire plane after expanding the domain to include negative numbers.

Video of the Day:

The Invention of Chess and $1+2+4+8+...+2^{63}=2^{64}-1$
This video mentions an old legend about the invention of chess and a neat problem that goes with it.

Analyzing exponential functions with different bases using the online Desmos graphing calculator

We demonstrate how the online Desmos graphing calculator can help students understand the behavior of some exponential functions.

Online Sources:

Khan Academy: Introduction to Exponential Equations

Additional Resource for Teachers:

If you wish to download the contents of this page as a printable pdf, click here: 6.3 Exponential Functions.pdf