Average Rate of Change
The average rate of change refers to the average rate at which a quantity or variable changes over a specific period of time or interval
The average rate of change refers to the average rate at which a quantity or variable changes over a specific period of time or interval. In mathematics, it is commonly used to measure the average steepness or slope of a line or function between two points.
To calculate the average rate of change, you need to determine the difference in the values of the variable or quantity over the interval and divide it by the difference in the corresponding input values. The formula for average rate of change is:
Average Rate of Change = (change in the variable) / (change in the input)
Let’s consider an example to understand this better. Suppose you have the following table with values for time (t) and distance (d):
| t | d |
|——-|——-|
| 0 | 10 |
| 2 | 30 |
| 4 | 50 |
| 6 | 70 |
To find the average rate of change of distance with respect to time between t = 0 and t = 6, we can use the formula:
Average Rate of Change = (change in d) / (change in t)
Here, the change in d is 70 – 10 = 60, and the change in t is 6 – 0 = 6. Plugging these values into the formula:
Average Rate of Change = 60 / 6 = 10
Therefore, the average rate of change of distance with respect to time between t = 0 and t = 6 is 10.
The average rate of change can also be interpreted as the slope of a line passing through the two points on a graph. In the example above, if we plot the points (0, 10) and (6, 70) on a graph, the average rate of change is equivalent to the slope of the line connecting these two points.
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