The average rate of change is 12 the interval from x=3 to x=5.
<h3>How to find the average rate of change of something?</h3>
Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
![\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
where when
![x = x_1, y = y_1\\and \\x = x_2, y = y_2](https://tex.z-dn.net/?f=x%20%3D%20x_1%2C%20y%20%3D%20y_1%5C%5Cand%20%5C%5Cx%20%3D%20x_2%2C%20y%20%3D%20y_2)
Given:
Interval; x = 3 to x = 5
We can represent these by
![x_1 = 3\\x_2 = 5](https://tex.z-dn.net/?f=x_1%20%3D%203%5C%5Cx_2%20%3D%205)
The corresponding y values are as follows
When x = 3, y = 8
When x = 5, y = 32
This will also be represented
![y_1 = 8\\y_2 = 32](https://tex.z-dn.net/?f=y_1%20%3D%208%5C%5Cy_2%20%3D%2032)
The average rate of change is then calculated as follows
![\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\\\m = \dfrac{32 -8}{5-3}\\\\m = \dfrac{24}{2}\\\\m = 12](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20rate%7D%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%5C%5C%5C%5C%5C%5Cm%20%3D%20%5Cdfrac%7B32%20-8%7D%7B5-3%7D%5C%5C%5C%5Cm%20%3D%20%20%5Cdfrac%7B24%7D%7B2%7D%5C%5C%5C%5Cm%20%3D%2012)
Hence, the average rate of change is 12.
Learn more about average rate;
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