8 - Rate of Change practice

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a quantity divided by the change in time or another variable. It is often expressed as a ratio.

Front

How do you calculate the average rate of change between two points?

Back

To calculate the average rate of change, use the formula: (f(b) - f(a)) / (b - a), where f(b) and f(a) are the values at points b and a, respectively.

Front

What does a positive average rate of change indicate?

Back

A positive average rate of change indicates that the quantity is increasing over the interval.

Front

What does a negative average rate of change indicate?

Back

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

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

The average rate of change is 75 feet per hour.

Front

What is the significance of the steepness of a graph in relation to rate of change?

Back

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

Front

In the context of a graph, what does a horizontal line represent?

Back

A horizontal line represents a rate of change of zero, indicating that the quantity is constant over that interval.

Front

How can you determine which section of a graph shows the fastest movement?

Back

The section of the graph with the steepest slope indicates the fastest movement.

Front

If Pete's height increases from 3 years old to 5 years old by 8 inches, what is the average rate of change?

Back

The average rate of change is 4 inches per year.

Front

What is the formula for calculating the rate of change in a savings account?

Back

Rate of change = (Final amount - Initial amount) / Time period.