A good example of the exponential function is a car crash. One would think that a sixty mph crash would be twice as bad as a Thirty mph crash, but it’s not. According to the National Safety Commission, a crash speed of 60 mph versus a 30 mph represents a 100 percent increase in speed; however, it increases the crash forces by 300 percent. What is the math here?
I would guess that this is statistical. At x mph y% of crash victims are killed, and when you plot that on a graph you get an exponential(ish) line. What do you mean by "crash forces?"
Its not exponential. It is quadratic. The kinetic energy of an object of mass m at speed v is \(\frac{1}{2}mv^{2}\). The KE of the same object at 2v is \(2mv^{2}\), which is 4 times as much. That's a 300% increase and if your brakes work with constant force it'll take 300% more distance to stop from speed 2v as it does at speed v.
