Rate of Change

Front

What is the definition of 'Rate of Change'?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often expressed as a ratio or a fraction.

Front

How do you calculate the rate of change?

Back

Rate of change = (Change in value) / (Change in time) or (Change in y) / (Change in x).

Front

If a car travels 60 miles in 1 hour, what is its rate of change in speed?

Back

The rate of change in speed is 60 miles per hour.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that the quantity is decreasing over time.

Front

If the water level is decreasing at a rate of 0.25 meters per hour, how much will it decrease in 4 hours?

Back

It will decrease by 1 meter (0.25 meters/hour * 4 hours).

Front

What is the significance of the slope in a graph representing rate of change?

Back

The slope of a graph indicates the rate of change; a steeper slope represents a greater rate of change.

Front

What is an example of a real-life situation that involves rate of change?

Back

The speed of a car, the growth rate of a plant, or the rate at which water is being drained from a tank.

Front

What is the formula for calculating average rate of change between two points on a graph?

Back

Average rate of change = (f(b) - f(a)) / (b - a), where f is the function and a and b are the two points.

Front

If a population increases from 100 to 150 in 5 years, what is the average rate of change?

Back

The average rate of change is 10 people per year ((150 - 100) / 5).

Front

What does it mean if the rate of change is constant?

Back

A constant rate of change means that the quantity changes by the same amount in each time interval.