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 Austin Stone. His topic, from Precalculus: solving exponential equations.

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

Exponential equations can be used in lots of different kinds of word problems. One that is pretty common but is very useful for students involves interest rate. “Megan has $20,000 to invest for 5 years and she found an interest rate of 5%. How much money will she have at the end of 5 years if the interest rate compounds monthly?” I would give them the formula A=P(1+r/n)rt. It is pretty easy to convince students that this is a real-world problem and would get the students engaged about exponential equations. You can also reword the problem to ask for how much Megan started with, what the rate is, or how much time the money was in there. That way students get used to solving equations when the variable is in the exponent and when it is not. This also can lead into or us prior knowledge of natural log to solve for the variable in the exponent.

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

Using the basis of the problem I mentioned above, a teacher could create a Project Based Instruction lesson using this idea. The teacher can set up a scenario where, over the course of a week or two, the students would have to decide which bank to make an investment in by calculating how much money they would profit at each bank. The students would have to research different banks and their interest rate. The teacher could also give each group different scenarios where some groups have more money to invest. Students would have to figure out how long they would like to invest. The teacher would give Do It Yourselves and Workshops that deal with solving exponential equations and also getting used to natural log. They would then make a presentation explaining what bank they have chosen and why. They would also have to explain the math that they would have used.

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How has this topic appeared in the news?

To say that exponential equations have been in the news lately would be an understatement. It has virtually been the news this year. COVID-19 is a virus and viruses spread exponentially. This would get students engaged immediately because the topic would be relatable to their own lives. Doctors and scientists try to figure out different ways to “flatten the curve”, which essentially means to make the spread of the virus not exponential anymore. We have all heard people on the news telling the public how to stop the virus from spreading and how not make people around you at risk of contracting it (contributing the exponential spread). We all have most likely seen a doctor or scientist show a graph of the virus’s spread and their predictions on how it will look in the upcoming weeks. This would give students a chance to see that what they are learning can be applied to very crucial things going on in the world around them.

References

Exponential Functions

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