average rate of change #2

Front

What is the average rate of change (ARC)?

Back

The average rate of change is a measure of how a quantity changes on average over a specific interval. It is calculated using the formula: ARC = (y2 - y1) / (x2 - x1).

Front

Calculate the average rate of change from (1, 3) to (5, 7).

Back

The average rate of change is (7 - 3) / (5 - 1) = 4 / 4 = 1.

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 car travels from 0 to 60 miles in 1 hour, what is its average rate of change?

Back

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

Front

How do you find the average rate of change between two points on a graph?

Back

To find the average rate of change, subtract the y-coordinates of the two points and divide by the difference of the x-coordinates.

Front

What is the average rate of change of a function f(x) = x^2 from x = 1 to x = 3?

Back

The average rate of change is (f(3) - f(1)) / (3 - 1) = (9 - 1) / 2 = 4.

Front

What is the significance of the average rate of change in real-world applications?

Back

The average rate of change helps to understand trends, such as speed, growth rates, and changes in financial data.

Front

If a rocket ascends from 1.5 miles to 8 miles in 120 seconds, what is its average rate of change in miles per second?

Back

The average rate of change is (8 - 1.5) / 120 = 0.0554 miles per second.

Front

What is the average rate of change of a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.