Average Rate of Change

Front

What is the Average Rate of Change (ARC)?

Back

The Average Rate of Change (ARC) measures how much a quantity changes on average over a specific interval. It is calculated using the formula: ARC = (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Front

How do you calculate the Average Rate of Change from a graph?

Back

To calculate the Average Rate of Change from a graph, identify two points (x1, y1) and (x2, y2) on the graph. Use the formula: ARC = (y2 - y1) / (x2 - x1).

Front

If Mrs. Taylor was 10 feet off the ground at 0 seconds and 20 feet at 5 seconds, what is her average rate of change?

Back

2 feet per second.

Front

What is the average rate of change of f(x)=3x-1 from 1 to 4?

Back

3.

Front

During which interval was the Jamison family's average speed the greatest?

Back

The first hour to the second hour.

Front

What is the formula for Average Rate of Change?

Back

ARC = (y2 - y1) / (x2 - x1).

Front

What is the average rate of change of y = 2(3)^x at [2, 4]?

Back

72.

Front

Define 'slope' in the context of Average Rate of Change.

Back

Slope represents the steepness of a line and is calculated as the change in y over the change in x (rise/run). In ARC, it indicates how much y changes for a given change in x.

Front

What does a positive Average Rate of Change indicate?

Back

A positive Average Rate of Change indicates that the function 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 function is decreasing over the interval.