# Engaging students: Solving exponential equations

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 Andrew Cory. His topic, from Precalculus: solving exponential equations.

B1. How can this topic be used in your students’ future courses in mathematics or science?

Solving exponential equations is important for students in their future courses. It can apply to mathematics courses in things like finances. Exponential growth is important for figuring out interest rates and how money will grow. It is also important for figuring out the growth rates of bacteria in science classes. This is the most common example used for solving exponential equations and it can help students with science classes they may take in the future.

A2. How could you as a teacher create an activity or project that involves your topic?

An activity that can be used to get students engaged in a lesson involving exponential equations and exponential growth, can be a quick example of a disease spreading. The teacher can select a student to start out “infected” and they stand up and walk around the classroom and tap a student on the shoulder. Now that student is also “infected.” Now the two students each tap a new person on the shoulder. Then those four people would go “infect” other students. Pretty quickly, the entire class will be standing up, “infected.” This is a good quick activity to get students to understand how the growth of exponential equations increases quickly. It also allows students to get up and move around, which is always good to do with how long students have to sit down during school.

C1. How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

Exponential equations have to do with the growth of any populations. One that became very popular recently is the idea of zombies. The idea of exponential growth happens with how rapidly the disease outbreak happens and how quickly the zombie population overtakes the human population. This idea grew in popularity exponentially a few years ago, but has since died out a bit. The idea of how rapidly a disease could spread was intriguing to audiences, but little did they know, they were learning about exponential growth while watching popular TV shows.

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