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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does a negative rate of change indicate?

Back

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

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.HSF-LE.A.1C

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.

Tags

CCSS.HSF-LE.A.1B