The average change is found using the formula (y2 - y1) / (x2 - x1), which essentially calculates the average rate of change between two points. Here's a breakdown:
Understanding the Formula
The formula (y2 - y1) / (x2 - x1) calculates the slope of a line connecting two points on a graph, representing the average rate of change between those two points.
- y1: The initial y-value.
- y2: The final y-value.
- x1: The initial x-value.
- x2: The final x-value.
This formula applies across many different disciplines as mentioned on 31-Jul-2023.
Steps to Calculate Average Change
- Identify Your Points: Determine the starting point (x1, y1) and the ending point (x2, y2). These points could represent time and distance, temperature changes, financial data, or any two-variable set where you are observing a change.
- Calculate the Change in y: Subtract the initial y-value (y1) from the final y-value (y2). This gives you y2 - y1. This is the net change in the y values.
- Calculate the Change in x: Subtract the initial x-value (x1) from the final x-value (x2). This gives you x2 - x1. This is the net change in the x values.
- Divide: Divide the change in y (y2 - y1) by the change in x (x2 - x1). The result is your average change.
Example
Let’s say you are tracking the growth of a plant. At day 1, the plant is 2 inches tall. At day 5, the plant is 10 inches tall.
- y1 = 2 inches (initial height)
- y2 = 10 inches (final height)
- x1 = 1 day (initial day)
- x2 = 5 days (final day)
Using the formula:
(10 - 2) / (5 - 1) = 8 / 4 = 2
Therefore, the average growth rate of the plant is 2 inches per day.
Applications of Average Change
The average rate of change can be applied in various contexts:
- Finance: Calculating the average change in stock prices over a period.
- Science: Determining the average speed of an object or average temperature change.
- Engineering: Analyzing performance of systems or components over time.
- Economics: Measuring the average change in prices or production.
Table Example
| Time (x) | Value (y) |
|---|---|
| x1 | y1 |
| x2 | y2 |
To calculate average change: (y2-y1)/(x2-x1)
