Have you ever noticed how hard it is to keep a secret? Maybe you tell one person and make them swear not to tell anybody, but then they tell somebody, and they tell somebody, and that person tells somebody, and pretty soon, it seems like everybody knows?

Using a mathematical expression containing exponents, you can see how quickly a rumor can spread from a single source to many, many sources. An expression containing exponents consists of two parts. The first part is the base. And the second part is the exponent.

So here we’ll call the base “b” and the exponent “n.” And an exponent is a shortcut; it’s a way to multiply a number by itself a certain number of times. So if we’re trying to figure out how a rumor spreads so quickly, the “b,” the base would be how many people have heard the rumor, and the exponent would be how many times the rumor’s been told. So for example, let’s say you know a rumor. And you tell two people. Well those two people can’t keep it a secret, so they each go and tell two people. And each of those two people tell two people. So using our expression, the first time the rumor is told, the exponent would be 1. And the base would be 2, because every time it’s shared, two people hear it. In the next round, each of those two people tells two people, so the exponent is now 2.

And finally, since this is the third time the rumor’s been told, the exponent changes to 3. So 2 x 1 is 2, 2 x 2 is 4, and 2 x 2 x 2 is 8. Two to the first plus two to the second plus two to the third is 14. So that rumor that you told to only two people quickly grew to 14 people knowing it, and as you can see, it doesn’t take long before pretty much everybody knows.