Exponential Growth and Decay

Several years ago, two close family members of mine died a very violent death. Their bodies were not discovered for two weeks, so naturally there was decomposition that occurred, making identification difficult. I will always be thankful for the law enforcement officers who understood the mathematics involved in exponential growth and decay, who helped us determine the time of death. Now, I can use this life experience, as awful as it was then, as the basis for a teaching activity.

My students are Algebra 2 and Pre-Calculus students. I discuss exponential growth in such varied areas as disease outbreaks (the spread of influenza, for example), population trends (for city planning) and cost appreciation (art work). Exponential decay covers depreciating valued items, such as office equipment or cars, as well as carbon dating fossils as I alluded to earlier.

In my classes, students would first learn about data collection, graphing data, and prediction equations. Next they would learn the criteria for determining whether a situation represents exponential growth or exponential decay and the formula work required for solving the problems.

In my dreams, this could be an interdisciplinary unit. I can envision enlisting the help of criminal justice students, studying crime scene investigations; the science department, analyzing samples; the history department could be involved in a field trip trying to search for artifacts in the area (quite a few Mastadon bones and other artifacts have been found in the local area, as the area was completely submerged under water in prehistoric times); TV productions could do an on-air commentary on the investigations; art could provide visual representations of any artifacts found; the English department could prepare research papers. As you can see, the possibilities for further study are endless.