Math: Applications for Living XVII

One of the big story lines in our ‘Math — Applications for Living’ course is percent change. The first level is comparing absolute and relative changes in quantities, along with percent increase and decrease expressions. We began to work on writing a mathematical model for percent increase or decrease as (1+r)^n, and saw compound interest as a variation on this. The course ends soon after we formalize this work by looking at exponential models for growth and decay.

Recently, I saw an article in our local newspaper that illustrated exponential growth in the world of internet traffic. With an accompanying story, the following graphic was used:

The original data is part of the Cisco IP modeling report (2011 to 2016); they have a report wizard at http://ciscovni.com/vni_forecast/index.htm

As you can see, the first and third graphs in the article are great examples of showing exponential change; the mobile data chart has the largest rate, but both graphs are delightfully exponential in nature. The problem is the middle graph — for corporate accounts. That graph is labeled “21% growth per year”, when the pattern is clearly linear; the data shows a slight decrease in growth rate later in the forecast period.

When we get to the exponential models in class, I plan to show this set of graphs in class and ask … ‘where is the error in this chart’. I think it is interesting that a journalist writing about internet trends does not understand exponential change enough to clearly communicate about two different patterns.

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