Blog 4: Finding the Average Rate of Change and Slope

Hello class, my name is Professor Eamon Martin, and I am here to teach you what the average rate of changeis, an example of the concept, and its' real world application. 

The average rate of change is the rate of change in q over the rate in change of in t.  It can also be thought of the difference between output values, as time is increased or decreased. 

To begin, we must first look at a given set of values.  Let’s say that we have these values for this particular situation: 

Year (t)	Sales of DVD's (in millions) (Q)
2000	3
2001	5
2002	8
2003	13
2004	25
2005	40
2006	60

As you can see, we do not have a linear growth rate amongst the values.  Instead, from year to year, we have different rates of growth.  In such a situation, we can find the Average Rate of Change, or the slope, for the entire set of data.

In order to do so, we take the last q value (in this case it is 60 million DVD’s sold) and subtract it by the first q value (3 million DVD’s sold).  This gives us 57 Million, or the change in Q.

We then subtract 2000 from 2006, giving us 6 years, or the change in t. 

As stated above, Rate of Change is change in Q over the change in t, so we input the values into their corresponding locations in the formula and get:

Change in Q   = 60-3           =   57   =     9.5 Million DVD’s sold per year

Change in T   2006-2000          6

Now I bet you’re wondering: “When am I actually going to need to use this concept?  I’m going to major in Art history, or International Relations, etc.?”

Being able to analyze data, and make projections is a skill that is useful in any discipline.  An employee for an Art store may look at the sales of pop art over the past several years, and may need to make projections regarding its sales in the future so that the store’s owner has better idea of whether or not to keep investing in similar products.  Similarly, an International Relations scholar may need to look at historical GDP growth rates for a Developed countries in order to make projections about the future health of their economies. Furthermore, being able to find the Average Rate of Change is something that you can show to your friends and family, that will make you feel smart and superior.  So there's that too!

Hopefully, with this lesson, you can advance your understanding of Average Rate of Change, and become a well equipped mathematican!