What characterizes an exponential function?

An exponential function is characterized by its specific equation form, which is f(x) = ab^x, where 'a' is a constant and 'b' is a positive base. In this form, the variable 'x' is in the exponent, indicating that as 'x' changes, the output of the function changes at a rate proportional to its current value. This leads to the characteristic rapid growth or decay seen in exponential functions, such as population growth or radioactive decay.

This unique structure sets exponential functions apart from other types of functions, such as linear and quadratic functions. A linear function, for example, would produce a straight line and is represented by a different form, while a quadratic function has a parabolic shape dictated by a second-degree polynomial. Furthermore, while a constant rate of change is a feature of linear functions, exponential functions demonstrate a variable rate of change, which accelerates or decays exponentially rather than linearly.