Rate of change
Key Notes :
1. Definition of Rate of Change
- The rate of change refers to how one quantity changes in relation to another. It is often expressed as the ratio of the change in the dependent variable to the change in the independent variable.
- It can be represented mathematically as
where Δy is the change in the dependent variable (y), and Δx is the change in the independent variable (x).
2. Common Examples of Rate of Change
- Speed: How distance changes with respect to time. Formula
Slope of a line: In a straight line, the rate of change of y with respect to x is represented by the slope (m):
where (x1,y1) and (x2,y2) are two points on the line.
3. Calculating Rate of Change
- Formula for rate of change:
- If you are given two points, (x1,y1) and (x2,y2), the rate of change can be calculated using the formula:
Units of Rate of Change: Depending on the situation, rate of change is expressed in units such as meters per second (m/s), kilometers per hour (km/h), dollars per item, etc.
Learn with an example
👉 Mrs. Green hosts an annual art contest for kids, and she keeps a record of the number of entries each year.
👉 According to the table, what was the rate of change between 2010 and 2014?
___ entries per year
- Plug the numbers into the formula for rate of change and simplify.
- Rate of change = change in value/change in time
- = 69 entries – 65 entries / 2014 – 2010
- = 69 entries – 65 entries / 4 years
- = 4 entries / 4 years
- = 1 entry per year
- The rate of change between 2010 and 2014 was 1 entry per year.
👉 Cameron kept track of how long it took to finish his homework each day.
👉 According to the table, what was the rate of change between Monday and Thursday?
_____ minutes per day
- Plug the numbers into the formula for rate of change and simplify.
- Rate of change = change in value/change in time
- = 52 minutes – 43 minutes / 3 days
- = 9 minutes / 3 days
- = 3 minutes per day
- The rate of change between Monday and Thursday was 3 minutes per day.
👉 A restaurant’s average food preparation time was tracked from day to day as part of an efficiency improvement program.
👉 According to the graph, what was the rate of change between Friday and Saturday?
_____ minutes per day
- Plug the numbers into the formula for rate of change and simplify.
- Rate of change = change in value/change in time
- = 43 minutes – 41 minutes / 1 day
- = 2 minutes / 1 day
- = 2 minutes per day
- The rate of change between Friday and Saturday was 2 minutes per day.
Let’s practice! 🖊️
