Exponential Function
f(x) = e^x
An exponential function is a mathematical function that grows or decays at a consistent rate. It is a function whose inputs, x, are used as the exponents of a particular base, b, and is defined by the following equation:
y = b^x
The base, b, is a positive constant and is typically greater than 1 if the function grows, or between 0 and 1 if the function decays. The exponent, x, can be any real number.
Exponential functions are widely used in science, economics, and social sciences to model phenomena that grow or decay exponentially. For example, population growth, radioactive decay, and compound interest can be modeled using exponential functions.
One important characteristic of exponential functions is that they grow or decay very quickly as x increases or decreases. For example, if the base is greater than 1, the function grows very quickly as x increases, and if the base is between 0 and 1, the function decays very quickly as x decreases.
There are several properties of exponential functions that are useful for understanding, analyzing, and graphing them, such as the domain and range of the function, the asymptotes, and the rate of growth or decay.
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