Compounding interest is the process where the value of an investment increases because the earnings on an investment, both capital gains and interest, earn interest as time passes. This exponential growth can be modeled using functions involving exponents.
Exponential Function: A mathematical function of the form $f(x) = a \cdot b^x$, where $b > 0$ and $b \neq 1$, describing growth or decay.
Logarithmic Function: The inverse function of an exponential function, often expressed as $y = \log_b(x)$.
$e$ (Euler's Number): $e$ is an irrational number approximately equal to 2.71828 and serves as the base for natural logarithms.