Average 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 represents how much a quantity changes on average over a specific interval.

Front

How do you calculate the average rate of change?

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 of the function at points b and a, respectively.

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 (700 - 400) / (6 - 2) = 300 / 4 = 75 feet per hour.

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

What is the slope in the context of average rate of change?

Back

The slope represents the average rate of change of a function over an interval and is calculated as the rise (change in y) over the run (change in x).

Front

Calculate the average rate of change from 20 to 40 minutes if the values change from 10 to 0 gallons.

Back

The average rate of change is (0 - 10) / (40 - 20) = -10 / 20 = -0.5 gallons per minute.

Front

What is the average rate of change from 10 to 30 minutes if the values change from 5 to 15 gallons?

Back

The average rate of change is (15 - 5) / (30 - 10) = 10 / 20 = 0.5 gallons per minute.

Front

If the average rate of change is -2 gallons per minute, what does this mean?

Back

This means that for every minute, the quantity decreases by 2 gallons.

Front

What is the formula for slope?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on a line.

Front

If the slope is -1/2, what does this indicate about the relationship between x and y?

Back

A slope of -1/2 indicates that for every 2 units increase in x, y decreases by 1 unit.