An exponential function is a mathematical function of the form f(x) = a * 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 one. Common examples include population growth and radioactive decay. Exponential functions have unique properties, such as the fact that their rates of change increase or decrease exponentially. They are widely used in various fields, including finance, biology, and physics, to model real-world phenomena like compound interest and the spread of diseases.