How do I find the power function that models a given set of ordered pairs?
1 Answer
First, let's remember what a power function is. For any constant real number
What does it mean that a power function
So, a given set of ordered pairs modeled by a power function corresponds to a set of points contained in the graph of the power function.
The problem becomes that of finding the equation of the power function given that we know the coordinates of a number of points of its graph. This is solved by solving the resulting system of equations.
Example:
Consider a given set of ordered pairs:
So, we have the following equations:
We see that
This is a simple illustration of the general idea. In practice, the problems can be more complex.