Half-exponential function

Okay, kiddo, so a half-exponential function is like having a toy that gets half as big every time you play with it.

Imagine you have a big ball and every time you bounce it, it gets half as big. The first time you bounce it, it's still pretty big. But if you bounce it again, it's only half as big as before. And if you bounce it a third time, it's only a quarter of the original size.

In math, we call this a half-exponential function because it's like having an exponent, which means multiplying by a number repeatedly, but only doing it halfway. So each time you multiply by half.

It looks like this: y = a(1/2)^x

The "x" tells us how many times we're going to multiply by half, and the "a" is just a number we start with. So if we start with "a" being 8 and we plug in "2" for "x", we get:

y = 8(1/2)^2

Which is the same as:

y = 8(1/4)

And that equals:

y = 2

So after bouncing the ball twice, it would only be 2 units big.

Does that make sense, kiddo?