Rate of Change

Front

What is the definition of rate of change?

Back

Rate of change is defined as the change in the value of a quantity divided by the change in another quantity, typically expressed as change of y / change of x.

Front

What does a rate of change of 0 m/s indicate?

Back

A rate of change of 0 m/s indicates that there is no change in position over time; the object is at rest.

Front

How do you calculate the average rate of change?

Back

The average rate of change is calculated by taking the difference in the values of the function at two points and dividing it by the difference in the input values: (f(b) - f(a)) / (b - a).

Front

If a climber ascends from 400 feet to 700 feet in 4 hours, what is the average rate of change in feet per hour?

Back

The average rate of change is (700 - 400) / (6 - 2) = 75 feet per hour.

Front

What is the average rate of change of Pete's height from 3 years old to 5 years old if he grew 8 inches?

Back

The average rate of change is 8 inches / 2 years = 4 inches per year.

Front

What is the significance of the slope in a rate of change context?

Back

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

Front

If Taylor can write 25 words per minute, how many words can he write in 10 minutes?

Back

Taylor can write 25 words/minute * 10 minutes = 250 words.

Front

What does a negative rate of change indicate?

Back

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

Front

In the context of a graph, what does the rate of change represent?

Back

The rate of change represents the steepness of the graph and how quickly the y-value changes with respect to the x-value.

Front

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

Back

The rate of change is 60 miles / 1 hour = 60 miles per hour.