In an earlier post, I shared a poster that I created using photos of odd numbers taken by local photographer mag3737. He shared this pictorial representation of the Pythagorean Theorem with me. Very cool – both the image itself and the online sharing.
The rate at which exponential functions grow can be a difficult concept to visualize. Starting at 2^4 = 16, the area is doubling but the height is not. By doing this, I’m not sure if I accomplished my goal of illustrating exponential growth (although I did manage to have the numbers fit on the page).
I suggest taking scissors to this poster. The eight columns of eight 64’s that represent 2^6 stacked on top of each other reach a height of over five feet. This is a powerful (and perhaps surprising?) image of exponential growth.
Instead, because of necessary scaling, students often see something like this: