Quiz and Comparing Linear, Exponential Models

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Objective

SWBAT compare linear and exponential growth models.

Big Idea

Linear models are used for situations involving change by a constant quantity while exponential models are change by a constant percentage.

Quiz on Representing Exponential Functions

45 minutes

Students will complete Quiz Switching Representations Exponential Functions in the first half of class.  This quiz assesses my students' ability to switch among the 4 representations of exponential functions: numerical, graphical, algebraic and verbal.

Linear or Exponential Growth?

45 minutes

In this lesson, I switch the focus from flexible algebraic and graphing work to real life applications of exponential functions.  I present each student with a copy of Linear Vs Exponential Growth Task from Illustrative Mathematics as an introduction to modeling with exponential functions.  My students have some background with this topic from Algebra 1, so I anticipate that they will be able to complete this task independently.  

When they have completed the task, we discuss linear and exponential models and how they differ. We take some notes on essential features of these two function types.  Some of the most important 

  • linear functions have a constant rate of change, while exponential functions have an increasing (or decreasing) rate of change
  • exponential growth always outpaces linear growth in the long run
  • linear growth is associated with increase by a constant quantity and exponential growth is associated with increase by a constant percent