average rate of change
The average rate of change is a mathematical concept that measures the average rate at which a quantity changes over a given interval
The average rate of change is a mathematical concept that measures the average rate at which a quantity changes over a given interval. It is calculated by finding the difference of the values of the quantity at the endpoints of the interval and dividing it by the difference in the corresponding input values.
To calculate the average rate of change, follow these steps:
1. Select the interval over which you want to find the average rate of change. This could be a time period, a distance, or any other relevant quantity.
2. Identify the initial and final values of the quantity at the endpoints of the interval. Let’s denote the initial value as y1 and the final value as y2.
3. Identify the corresponding input values (usually denoted as x1 and x2) at the endpoints of the interval.
4. Calculate the difference in the values of the quantity: y2 – y1.
5. Calculate the difference in the input values: x2 – x1.
6. Divide the difference in the values (step 4) by the difference in the input values (step 5).
The formula for average rate of change can be written as:
Average rate of change = (y2 – y1) / (x2 – x1)
Here’s an example to illustrate how to calculate average rate of change:
Consider a situation where the number of customers at a store is recorded at the beginning and end of each day. Let’s say that on the first day (x1), there were 100 customers (y1), and on the third day (x2), there were 200 customers (y2).
Average rate of change = (y2 – y1) / (x2 – x1)
= (200 – 100) / (3 – 1)
= 100 / 2
= 50
Therefore, the average rate of change in the number of customers per day is 50. This means that, on average, the number of customers is increasing by 50 per day.
Remember that the average rate of change provides a measure of the overall change of a quantity over an interval. It does not tell us about the specific behavior of the quantity at different points within the interval.
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