In eighth grade Algebra I (Advanced), we have been studying exponential functions: numerical relationships that grow by multiplication. This is a great opportunity for our class to discuss and learn about finances and interest rates! In one of the lessons we worked on this week, students worked on a series of problems where the characters had invested money in an account earning 5% annual interest, meaning that the total balance increased by a factor of 1.05 each year. Students already know how to use an exponent on a number like 1.05 to calculate the total balance several years in the future.
In our current unit, they are learning how to work with negative exponents to calculate balances in previous years, and with fractional exponents and roots to calculate precise balances mid-year. We also took some time to talk about the extent to which mathematical models like this do and do not match real-world investing situations. It’s always a joy to weave back and forth between the sometimes theoretical world of pure mathematics and the practical mathematics that we encounter beyond the classroom.
