# Engaging students: Exponential Growth and Decay

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Megan Termini. Her topic, from Precalculus: exponential growth and decay. How could you as a teacher create an activity or project that involves your topic?

A fun and engaging activity for students learning about exponential growth and decay would be a zombie activity. The students will get a scenario about the zombie attacks and they will predict the way the zombie attacks will work. Then to begin, the teacher will be the only one infected and to show the infection, they will have a red dot on their hand. Then they will shut off the lights and turn them back on to indicate a new day. Then the teacher will “infect” one other student by putting a red dot on their hand. Then they will turn the lights off and turn back on for day 2. Then both the teacher and the infected student will both go “infect” one other person. Then it continues day by day until everyone in the class is infected. Then they will put their data in a table, graph it and can see that it is an exponential growth, then write an equation for it (Reference A). This is great way of getting the whole class involved and zombies are very popular with tv shows and movies. It also lets them explore, see the pattern, and try to come up with the equation on their own. How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

A great use of technology for graphing exponential growth and decay is Desmos. Desmos lets the students take an equation and plug it in to see the graph. They are also able to change the window to see it better. It also will give you the table for the function that you inputted. It’s good for students to graph it on here to see the graph and also, they are able to click anywhere on the graph to see the point they want. This also would be a good program for them to check their work after trying the problem on their own first (Reference B). Another great website is Math Warehouse. This website lets students explore the graph of exponential functions. Students can type in their function and can graph it. It also lets you compare it to y=x, y=x2, and y=x3. It also has the properties for exponential growth and decay. This website is great for students to interact with exponential functions and also explore them (Reference C). How can this topic be used in your students’ future courses in mathematics or science?

Exponential functions stay with you all through your school career. You use them in many mathematics courses like algebra, algebra 2, pre-calculus, calculus, etc. You also use them in science courses like biology, chemistry, physics, etc. Understanding how to graph exponential growth and decay functions is a very important tool for future courses. For example, in algebra 2 the students will be learning about logarithms and exponentials, and will have to graph both of them and know the difference between them. Another example is in biology, comparing the number of births and the number of deaths of a species. The data may show an exponential growth in the number of births and exponential decay in the number of deaths, and the students would need to know how to plot the data points and graph it. It is also important for them to understand what the graph means and not just how to graph it. These are skills students will need in not only their future mathematics and science courses, but also in their future careers. For example, a biologist who studies a species of animals might have an exponential decay of the animal and would track its progress every week or every day and graph it to show the decrease of the amount of that species. Many students may not realize it now, but graphing exponential growth and decay is an important topic to understand how to do and why it is important to learn.

References:

A. “Zombies: Exploring Exponential Growth.” BetterLesson, betterlesson.com/lesson/460610/zombies-exploring-exponential-growth.
B. “Exponential Growth and Decay.” Desmos Graphing Calculator, http://www.desmos.com/calculator/d7dnmu5cuq.
C. “Interactive Exponential Function Graph/Applet.” Exponential Growth/Decay Graph Applet . Explore graph and equation of exponential functions| Math Warehouse, http://www.mathwarehouse.com/exponential-growth-and-decay/interactive-exponential-graph-applet.php.