Exponential Curves

Hands-On Approach to Exponential and Logarithmic Functions

Four different curves that match y = b^x where the base, b, is either 2, e, 3, or 10. To identify the base, each model has the number included at the part of the curve that goes toward the asymptote. These could also be used for y = log_b (x) curves. Match two together to show the reflection across y = x. See second slideshow in photos.

To facilitate printing for class sets, I included STL files with the models grouped in sets of 10 and 40. These work well for faster setup. See my image for printing 50 at a time (a set of 10 and a set of 40 together). Be sure to print extras for a class set!

---

Inspiration

Anticipating a lesson on exponential functions with my 9th grade students, I wanted to find a way for them to get a better feel of the shape of the curve. These worked great!! Each student had one in their hands along with blank coordinate axes. When discussing the characteristics of exponential functions, we would use the model to make predictions about the direction and location of the curve before graphing it more precisely. In the next lesson, some students chose to use the models again to help them figure things out.

I realized a I needed a model for myself to hold at the front of the class and on the board for demonstrations. I printed the "Base 3" model at 400% scale. So fun!!

Bonus: I also included a PDF file with two sets of blank coordinate axes. These worked well in class. There is also a PDF file with a note that I gave to the teachers when I made them a class set.

---

Mathematical Models

• This model is featured in my 3DWithUs article!
  3D Printable Math Models for Teaching Complex Concepts

• Find more models for mathematics in my Math Surfaces, Solids, Etc. Collection.

---