## Average rate of change

### The average rate of change refers to the ratio of the change in a quantity to the corresponding change in another quantity over a specific interval

The average rate of change refers to the ratio of the change in a quantity to the corresponding change in another quantity over a specific interval. It is used to measure how much a quantity is changing on average per unit of time or distance.

To calculate the average rate of change, you need to determine the difference between the initial and final values of the quantity you are interested in, and divide it by the difference in the corresponding values of the other quantity. This can be expressed as:

Average Rate of Change = (Change in Quantity) / (Change in Other Quantity)

For example, let’s say we are interested in finding the average rate of change of the distance covered by a car over a time interval. If the distance the car traveled initially was 50 miles and the final distance was 150 miles, and the corresponding time interval was 2 hours, then the average rate of change would be:

Average Rate of Change = (150 – 50) miles / (2 – 0) hours

= 100 miles / 2 hours

= 50 miles per hour

So, in this example, the average rate of change of the car’s distance traveled is 50 miles per hour.

The average rate of change can be used to analyze various situations in mathematics, physics, economics, and other fields. It is a useful tool to understand how quantities change over time or with respect to other variables.

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