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 Elizabeth (Markham) Atkins. Her topic, from Precalculus: solving exponential equations.

A.   APPLICATIONS: What interesting (i.e., uncontrived) word problems using this topic can your students do now?

Exponential equations can be different topics. You can use exponential equations for bacterial growth or decay, population growth or decay, or even a child eating their Halloween candy. Another example would be minimum wage.  A good word problem would be at one point minimum wage was $1.50 an hour. Use A= to figure out when minimum wage will reach $10.25 an hour. Another good word problem would be Billy Joe gets a dollar on his first day of work. Every day he works his salary for that day doubles. How much money does he have at the end of 30 days? A good money example would also be banking. “Use the equation . Shawn put $100 in a savings account, which has a rate of 5% per year. How long will it take for his savings to grow to $1000? There are many ways to show exponential growth and decay.

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

Exponential equations can be used in science and life for many years from now.  Students will see exponential equations when they begin to study bacteria. They will have to find the decay of growth. Students will also have to see population growth and decay throughout history. They may be asked to find out what the population will be in twenty years. When students take economics, or do their own banking, they will need to calculate interest and principal. Students will also need to do the stock market which uses exponential equations. If students go into field where they are concerned with the population of species that may be becoming extinct then the student would predict when the species would become distinct by using an exponential formula. They could also calculate how long until a certain species may take over the world, such as tree frogs or rabbits. Exponential equations are everywhere in the world and in other subjects, besides mathematics.

E. TECHNOLOGY: How can technology (YouTube, Khan Academy [khanacademy.org], Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

Exponential equations are used with technology everyday and every which way. Khan Academy has a few examples of exponential growth and exponential decay. Youtube has many great examples of exponential equations. Crewcalc’s exponential rap is an excellent example. They are very creative high school who found a way to express a mathematical concept through music.

Zombie Growth shows another interesting way to portray the mathematical concept of exponential equations. They use the phenomenon of zombies to demonstrate how exponential equations work.

Math project on Youtube showed another way to demonstrate how exponential equations work. They posed a problem and then stated the steps to solve the problem. Students need to use graphing calculators to check whether or not they have the right graph based on information given. They also need calculators to calculate equations and check their equations.