What describes an exponential function?

An exponential function is characterized by its specific mathematical form expressed as f(x) = a*b^x, where 'a' is a non-zero constant, 'b' is a positive constant base (with b ≠ 1), and 'x' is the exponent. This form captures the essence of exponential growth or decay, as the output of the function (the value of f(x)) increases or decreases rapidly based on the value of 'x'.

In an exponential function, as 'x' increases, the function value changes at an increasing rate when b > 1, leading to growth that accelerates, while if 0 < b < 1, the function decreases, but at a decreasing rate, indicating decay. The fundamental quality of the exponential function is its reliance on the variable exponentiation of the base, distinguishing it from other types of functions, such as linear functions. Therefore, option A accurately describes what constitutes an exponential function.