# Average Rate of Change Definition

In Mathematics or Finance, the average rate of change is defined as the ratio between the change in input by the change in output. In other words, it is narrated as determining how much an object may vary over time. For instance, if the gas price increases by about 19.6$ each year, it means the average rate of change is the price of gas a year ago by change is the price of gas now.

**Table of Contents**

## Formula of Average Rate of Change

The formula used to find the average rate of change is listed below:

The average rate of change = change in output / change in input.

**Note:**

To calculate the average rate of change, you can use our Average Rate Of Change Calculator.

### Example

Suppose we run a petroleum agency and want to calculate the average rate of change in the petrol price from 2010 to 2013. Using the date below in the table will figure out the solution.

y | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
---|---|---|---|---|---|---|---|---|

C (y) | 2.31 | 2.62 | 2.84 | 3.30 | 2.41 | 2.85 | 3.20 | 3.68 |

**Given data**

From the graph, we can see that in 2010 the price was $3.30, whereas, in 2013, the price is increased by $3.20.

**To Find**

Average rate of change = ?

**Solution**

To find the potential energy, we can use the formula listed below:

The average rate of change = change in output / change in input.

The average rate of change = Δy/Δx = (y_{2}- y_{1})/(x_{2}- x_{1})

Putting values in the formula:

AROC = (3.20 - 3.30)/(2013 - 2010)

AROC = (-0.10)/(3)

AROC = -0.033 / year