Compare rates of growth between an exponential function and a power function for positive x-values.
- For positive values of x, students will identify the following behaviors of exponential and power functions:
- For large (x>a) x-values, exponential functions of the form y =ax grow faster than power functions of the form = xa
- For particular x-values, power and exponential functions can be equivalent
- On certain intervals, power functions can have greater value than exponential functions
- Exponential function
- Power function
About the Lesson
This lesson involves comparing rates of growth between the exponential function f(x)=ax and the power function g(x)=xa for positive x-values. As a result, students will:
- Compare the discrete value of these functions for a = 2, 3, 4, and 5 as x moves along a number line from 1 to 5.
- Compare the graphs of the functions for a = 2, 3, 4, and 5 as x moves along the x-axis.