An exponential function is a mathematical function of the form f(x) = a * bx, where:
- a is a constant that represents the initial value or the y-intercept of the graph.
- b is the base of the exponential, and it must be a positive real number not equal to 1.
- x is the exponent, which can be any real number.
The key characteristic of exponential functions is that they grow (or decay) at a rate proportional to their current value. This means that as x increases, the value of f(x) increases (or decreases for decay) more rapidly. Exponential functions can model a variety of real-world phenomena, such as population growth, radioactive decay, and interest compounding.