Power Tools By STEVEN STROGATZ
But when you need mathematical dynamite, it’s time to unpack the exponential functions. They describe all sorts of explosive growth, from nuclear chain reactions to the proliferation of bacteria in a Petri dish. The most familiar example is the function 10x, in which 10 is raised to the power x. Make sure not to confuse this with the earlier power functions. Here the exponent (the power x) is a variable, and the base (the number 10) is a constant — whereas in a power function like x2, it’s the other way around. This switch makes a huge difference. Exponential growth is almost unimaginably rapid.
That’s why it’s so hard to fold a piece of paper in half more than 7 or 8 times. Each folding approximately doubles the thickness of the wad, causing it to grow exponentially. Meanwhile, the wad’s length shrinks in half every time, and thus decreases exponentially fast. For a standard sheet of notebook paper, after 7 folds the wad becomes thicker than it is long, so it can’t be folded again. It’s not a matter of the folder’s strength; for a sheet to be considered legitimately folded n times, the resulting wad is required to have 2n layers in a straight line, and this can’t happen if the wad is thicker than it is long. […]
The rest of the article is worth reading; I’ll probably send it to my “business calculus” students.