Math

The average rate of change.

Presented by Kaiden Benoit.

What is rate of change?

In mathematics, the average rate of change is a measure of how much the function has changed per unit. Here are a few examples to the right:

​Also, some vocabulary words that may and most likely will be used while doing average rate of change are: Slope, y-intercept, and of course, rate of change.

Multiple Choice

What is Mrs. Gordon's rate from 0 to 2 seconds?

• 2.5 feet per second
• .4 feet per second
• 5 feet per second
• .2 feet per second

So what's the explanation?

​It's actually pretty simple:

You can solve this problem by assessing the situation in this way. First, you look at how much the distance has been increased by once you are in the 2 seconds row. We see that the distance has increased by 5ft after 2 seconds, so to find out how many ft per second was gained, we simply divide 5 by 2, getting 2.5ft per second.

Multiple Choice

What is the average rate of change of the average height in feet of the trees with respect to the number of years since the trees were planted?

• 3 ft/yr

• 7 ft/yr

• 10 ft/yr

• 14 ft/yr

​How do we solve this problem?

So the first step to this is to know how many feet increased over two more years. We know that the first year begins at 10, so our answer is a number that has to be multiplied twice to get to 3 years. So we would have to figure out x times two plus 10 to get our answer. 7 x 2 = 14 + 10 = 24. Thus, our answer is 7.

Try some on your own!

Multiple Choice

Calculate the average rate of change from 20 to 40 minutes.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

THANK YOU, GOODBYE!!!

Multiple Choice

Find the average rate of change of Pete's height from 3 years old to 5 years old.

• 2 inches per year
• 8 inches per year
• 2 years
• 4 inches per year

Multiple Choice

At 0 seconds, Mrs. Taylor was 10 feet off the ground.  At 5 seconds, she was 20 feet off the ground.  What is her rate in feet per second?

• 10 feet per second
• 5 feet per second
• 2 feet per second
• 6 feet per second

Multiple Choice

Average Rate of Change is also known as...

• y-intercept
• x-intercept
• linear
• slope

Kaiden Benoit.

" Now, it is time for homework." 

Don't worry, it's easy:

​Create and solve one problem regarding this topic.

Using the knowledge you gained from this presentation, create one average rate of change problem and work out how you solved it on paper.