Average Rate of Change Calculator

Formula

The formula to calculate the Average Rate of Change (AROC) is:

\[ AROC = \frac{Y2 - Y1}{X2 - X1} \]

Where:

\( AROC \) is the Average Rate of Change
\( Y1 \) and \( Y2 \) are the values of the function at \( X1 \) and \( X2 \) respectively
\( X1 \) and \( X2 \) are the x-coordinates of the points

What is Average Rate of Change (AROC)?

AROC measures the average rate at which a quantity changes over a specific interval. It is analogous to slope but is used more broadly to describe changes in non-linear functions or quantities.

AROC is essential in analyzing trends in various fields such as economics, biology, physics, and more, where understanding how variables change over time or in relation to other variables is crucial.

Example Calculation

Given:

\( X1 = 2 \), \( Y1 = 5 \)
\( X2 = 5 \), \( Y2 = 12 \)

Calculate AROC:

\[ AROC = \frac{12 - 5}{5 - 2} = \frac{7}{3} = 2.3333 \]

Therefore, the average rate of change (AROC) between these two points is approximately 2.3333.