# FUNCTIONS WITH SETS OF DATA: EXPONENTIAL MODELING

This guide illustrates how to use an input/output table when given any type of function. In addition, this guide uses formulas and concepts to create models representing a given set of data.

## INTRODUCTION

From business to engineering to cooking to fashion, data is everywhere. Sets of data can inform us about past, present, and future time periods and how those time periods impacted our career or business. Sets of data can be organized into a model, which can better serve you, your employees, and/or a future investor. Creating a exponential model from a set of data creates an efficient line of communication that helps people understand what a set of data represents.

## WHAT IS AN EXPONENTIAL MODEL?

Compared to a linear model, an exponential is NOT a straight line. Exponential graphs have a curve like a boomerang or crescent moon. Be careful! There are graphs that have curves as well.

## FOUR COMPONENTS

There are four components of an exponential model:

1. Independent/Input: Any number you plug into a function. These numbers can be used as x-coordinates.
2. Dependent/Output: We can plug any number into a function. After we calculate the function, our answer is our output. These can be used as y-coordinates when graphing.
3. Rate of Change (a): The rate of change is different from a linear model because it is NOT a constant change between coordinates. Using the formula in the model provided on the left, you can calculate the value.
4. Y-Intercept: Input is ALWAYS 0. Depending on the scenario, this is most likely the starting point.

## NOTES, EXAMPLES, AND A REAL LIFE APPLICATION!

Here are some quick notes:

Here is a video with examples: