An exponential function is a mathematical function of the form f(x) = a \cdot b^x , where a is a constant, b is the base (a positive number), and x is the exponent. These functions are characterized by their rapid growth or decay, depending on whether the base b is greater than or less than 1. Common examples include population growth and radioactive decay. Exponential functions are widely used in various fields, including finance for compound interest calculations, biology for modeling population dynamics, and physics for describing processes like radioactive decay. Their unique properties make them essential for understanding complex systems and phenomena.