The simplest growth is linear or arithmetic. If a car traveling at a constant speed goes 40 miles in one hour, then it will go 80 miles in two hours. Doubling the time doubles the distance. But if you drop a stone down a well to see how deep it is, a one-second fall before you hear a splash means the water is about 16 feet down, whereas a two-second fall means the water is 64 feet down. Doubling the time quadruples the distance. Distance goes up with the square of time. This is called polynomial growth.
I recently read a book that claimed the destructive power of hurricanes “increases exponentially with wind speed.” That's not true. Hurricane power increases with the cube of wind speed—doubling the wind speed causes eight times the destruction. This is also polynomial growth, of degree three as opposed to the stone falling, which is of degree two.
If hurricane power were exponential, a first doubling of the wind speed could result in eight times the destruction, but the second doubling would increase power 64 times, the third one 512 times, and the fourth one 4,096 times. With cubic polynomial growth, in contrast, every doubling leads to the same eightfold increase in power.
Cubic polynomial growth is scary enough. Ten-mile-per-hour wind is a gentle breeze, 20 mph is a fresh breeze, 40 mph is a gale, 80 mph is a category 1 hurricane—like Hurricane Dolly, something that wipes out badly constructed mobile homes, breaks windows, and damages chimneys—and 160 mph is ...