e^x function

The function \( e^x \) represents exponential growth or decay, where a quantity increases or decreases at a rate proportional to its current size. The base \( e \) (approximately 2.718) is a special constant related to continuous growth processes, like compound interest or population increase. When you input a number \( x \), \( e^x \) gives you the value after applying this continuous growth over \( x \) units of time or space. It’s unique because its rate of change (derivative) is the function itself, making it fundamental in calculus and many natural phenomena.