# Average Rate Of Change Calculator

The variation in y-value by variation in x-value for both distinct points on the graph is known as the average change rate for function.

In simple words,

The average rate of change is the change in the rate of a quantity divided by the total time.

Or,

The change in rate per year is known as the rate of change because it narrates how output volume changes relative to the alteration in input volume.

If you use the required first and last input-output volumes data, you can easily find the Average rate of change.

## Average Rate Of Change Calculator Representation

To find the average rate of change, we divide the output rate variation by variation in the input rate.

Average rate of change = change in output/change in output

In mathematical form it is written as follow;

Average rate of change => AROC = Δy/Δx

AROC= (y_{2}- y_{1})/(x_{2}- x_{1})

= [f(x_{2}) - f(x_{1})]/x_{2}- x_{1}

- The change in value is demonstrated by the Greek letter Delta
**(∆)**. - So the ratio is read by delta y over delta x.
- ∆f Symbolize ∆y, changing the function doesn’t mean it changed the value of the output function.

### 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 |

### Solution

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

Using the formula of the average rate of change,

Δy/Δx = (y_{2}- y_{1})/(x_{2}- x_{1})

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

AROC = (-0.10)/(3)

AROC = -0.033 / year

The decrease of **-0.033/year** is known as a negative change or a negative increase. When output decreases as input increases, this rate of change is known as negative change.

### Calculator use

Using the Average rate of change calculator, you can find the solution without doing any self calculations. Just enter the input and output values. After that, our algorithm will find the optimum solution for you.