This week I am teaching my lessons on exponential and logarithmic functions. These lessons are always interesting. My students are not allowed to use calculators so they are “encouraged” to think about these functions and how they behave algebraically, which can be challenging.
I begin my lessons with a general exponential function f(x) = ax (for a > 0, a ≠ 1). I discuss how the function behaves for a > 1 and 0 < a < 1. I present the graphs of both and solicit engagement from my students while discussing the properties of the functions (and their corresponding graphs).
Next, I introduce logarithmic functions as the inverse function of exponential functions. I use the properties of inverse functions to graph the general logarithmic function f(x) = loga(x). Once the graph is complete, I discuss the properties of logarithmic functions with my students.
These concepts are usually difficult to grasp since most students are not used to thinking about math concepts in-depth. This is the point in the semester where students begin to ask the big question: “How is this used in the real world?” One student wanted to know if exponential and logarithmic functions are useful for real-world situations. I told him they are and shared a few basic examples in class. Of course the discussion motivated me to write this blog.
Here are a few practical uses for exponential and logarithmic functions:
Population Growth (the rate of growth of people, animals, etc.)
Exponential Decay (the rate of decay of organisms)
Compound Interest (the rate of growth of an interest bearing account)
Mortgage Payments (the rate of growth of interest on a mortgage account)
Earthquakes (their magnitude)
pH (a solutions level: acidic vs. basic/alkaline)
Decibel of Sound (the measure of sound levels)
There are so many practical uses for both functions, but I listed the most relevant uses for my students. Most of my students should be able to relate to at least one item from the lists. More information can be obtained by conducting a little research.
What are other practical uses for exponential and logarithmic functions?