Introduction to Exponential Functions

 Introduction:

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

 Learning Objectives:

• In the story about the legendary origins of chess in India Links to an external site., 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?