Exponential function

An exponential function describes a process where a quantity grows or shrinks at a rate proportional to its current size. Think of it as compound interest on a bank account: each period, the amount increases by a fixed percentage, leading to rapid growth over time. Conversely, it can model processes like radioactive decay, where a substance decreases by a percentage regularly. Mathematically, it's written as \(f(x) = a \times b^x\), where \(a\) is the starting amount, \(b\) is the growth or decay rate (greater than 1 for growth, between 0 and 1 for decay), and \(x\) is the time or step.