## average rate of change

### The average rate of change is a mathematical concept used to measure the average rate at which one quantity is changing with respect to another over a given interval

The average rate of change is a mathematical concept used to measure the average rate at which one quantity is changing with respect to another over a given interval. It is also known as the average rate of variation.

To calculate the average rate of change, you need to consider two values of the quantity you are observing, let’s say “y”, at two different points in time or positions, represented by “x”. The average rate of change is then determined by finding the difference in the values of “y” between the two points, and dividing it by the difference in the values of “x”.

Mathematically, the formula for average rate of change is:

Average Rate of Change = (change in y) / (change in x)

Let’s take an example to illustrate this concept. Suppose you are monitoring the growth of a plant over a period of 5 days. On the first day (x = 1), the plant’s height is measured to be 10 cm (y = 10), and on the fifth day (x = 5), the plant’s height is measured to be 30 cm (y = 30).

To find the average rate of change in the plant’s height over this 5-day period, you would calculate:

Average Rate of Change = (30 – 10) / (5 – 1) = 20 / 4 = 5 cm per day

Therefore, the average rate of change in the plant’s height over the 5-day period is 5 cm per day. This means that, on average, the plant’s height is increasing by 5 cm per day during this time frame.

The average rate of change can be applied to various scenarios, not just in the context of time. It is useful in many fields such as physics, economics, and engineering to analyze and understand how one quantity changes with respect to another.

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