What kind of mathematical operation is used to repeatedly increase a number by a certain percentage?

Question

I am sure that this is an easy question to answer for most of you.

I need to take a number, let's say $10$, and then increase it by a percentage, let's do $25\%$.

$10 \times 1.25 = 12.5$

Easy enough, but I need to repeat that several times using the product of the previous iteration:

$10 \times 1.25 = 12.5$

$12.5 \times 1.25 = 15.625$

$15.625 \times 1.25 = 19.53$

$19.53 \times 1.25 = 24.41$

. . .and so on.

What is this type of operation called? At first I thought it would be a type of logarithm but that didn't seem right.

Admittedly, my foundation in math isn't what I would like for it to be. . .thanks for your help.

Answer 1

Its like compound interest! The general formula would be $10 \times 1.25^n$ where n is the amount of times you are "compounding the interest".

Answer 2

This is exponentiation, denoted $x^y$, meaning $x * x$, $y$ times, so $10 * 1.25 * 1.25 * 1.25$ is $10 * 1.25^3$.