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 (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2).

Front

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

Back

Rate of Change = 60 miles / 1 hour = 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

Decrease = Rate of Change x Time = 0.25 meters/hour x 4 hours = 1 meter.

Front

What is the significance of the slope in a graph?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is an example of a real-world 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 the average rate of change between two points on a graph?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a) where a and b are the x-values of the two points.

Front

If a population of bacteria doubles every hour, what is the rate of change?

Back

The rate of change is exponential, meaning it increases rapidly as time progresses.

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.