Exponential and Decay Functions

  At some point, we teach students about exponential and decay functions.  The goto examples for exponential functions is unlimited population growth be it people or bacteria but what are some other possibilities for exponential growth?

Exponential growth formulas are used when something grows at a certain percentage every year while exponential decay are used for situations where something decreases a specific percentage every year.

One that is fairly new, is the growth of social networks such as Facebook.  Since 2004, these social networks have experienced an exponential growth.  Facebook itself has gone from one million members in 2004 to over a billion in 2010.  That means if Facebook were a country it would be the 3rd largest country in the world.

Other companies with exponential growth include Uber transportation and AirBnB companies.  Ideas which just took off.  For instance Uber has grown from $200,000 in 2009 to $1,200,000,000 in 2014 while AirBnB has only grown from 7.2 mill.  Image giving students these figures and letting them figure out the formula?  That could be fun because it students are looking at real companies.

The United States Gross Domestic Product per capita has grown at a steady rate of  two percent per year for almost two centuries.   Another area with exponential growth is continuous interest on money investments.  Its always interesting to compare continuous interest with simple interest to see how much of a difference there really is when all is said and done.  My students have been surprised by that.

One thing I found interesting that is an exponential growth is the increase of computing power.  its said by 2030, the computing power of a computer will equal that of the human brain. Even consumption of fuel has exponentially grown over the past couple of centuries.

Then if you look at the negative exponential functions often referred to as decay there is the old radio active decay situation but many of my students do not relate to that.  Instead bring up how coroners use negative exponential functions to determine the time of death using a specific formula.  

One of these decay situations involves a bill that a politician tried to pass which would force restaurants to decrease the amount of salt used in cooking by two and a half percent each year.  The politician tried to pass this law because people have been consuming too much salt but the law did not pass.

In addition, the decay formula is used to calculate the amount of formula on a loan whose balance is decreasing.  If students ever look at mortgage payments They will notice that most of the payment at first is to pay off the interest while at the end it changes to be mostly principal. 

Further more, the value of cars is considered to be an exponential decay as it ages because its value decreases the longer you own the car. 

So many situations other than population and half life situations.  I'd love to teach this next year by having students choose a specific situation, find the formula for the situation and then create a short video to present their information.

Let me know what you think. I'd love to hear.