FYI, exponential decays...decay
. That's hardly the signature of something that is "uncontrollable." Chain reactions for thermonuclear explosions depend on exponential growth
. Think about it.
An exponential decay is the necessary logical consequence of an extremely simple thing: If a fixed percentage
of atoms decay (equivalently, if the probability of a given fraction atoms decaying is fixed -- stays the same) within a given interval, you get an exponential
. It's precisely the same behavior you would observe if your bank balance lost a fixed percentage every day, for example, with no replenishing of funds. This is what Harold 14370 was telling you.
Work it out mathematically, maybe with an example with specific numbers first. Start with 100 dollars, say. Suppose you lose 10% each day. So the day-by-day bank balances are in a sequence like this: 100, 90, 81, 72.90, 65.61...Plot the sequence. You will find that the points conform to those of an exponential curve.
Want the math? Here's a capsule summary: Saying that a fixed percentage of atoms decay per unit time is equivalent to saying that dN/dt is proportional to N, where N is the number of atoms. So set dN/dt = BN, where B is a constant, and solve (B will have a negative sign if you are talking about decay, and a positive sign if you are talking about growth). You can verify that an exponential is a solution to the simple equation.
Now the only difference is that, in actual fact, radioactive decay is probabilistic, so "given interval" must be interpreted stochastically. But the math is the same -- you get an exponential.