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 as the change in the output value divided by the change in the input value.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the formula for calculating ARC?

Back

The formula for Average Rate of Change is: ARC = (y₂ - y₁) / (x₂ - x₁)

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If Pete's height increased from 40 inches to 48 inches from age 3 to age 5, what is the average rate of change?

Back

4 inches per year

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change from x=0 to x=1 if f(0) = 2 and f(1) = 5?

Back

3

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Calculate the average rate of change of the function f(x) = 2x + 1 from x=1 to x=3.

Back

The average rate of change is 2.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a car travels from 60 miles to 100 miles in 2 hours, what is the average rate of change in speed?

Back

20 miles per hour

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Find the average rate of change of the function f(x) = -x² + 4 from x=0 to x=2.

Back

The average rate of change is -2.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If the temperature changes from 30°F to 50°F over 4 hours, what is the average rate of change in temperature?

Back

5°F per hour

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6