Exponential and Logarithmic Functions
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Exponential Functions
Exponential functions are functions of the form f(x) = a^x, where a is a positive constant called the base. Exponential functions are increasing when a > 1 and decreasing when 0 < a < 1. The graph of an exponential function is a curve that approaches the x-axis as x approaches negative infinity and increases without bound as x approaches positive infinity.
Logarithmic Functions
Logarithmic functions are the inverse of exponential functions. They are functions of the form f(x) = loga(x), where a is a positive constant called the base. Logarithmic functions are increasing when a > 1 and decreasing when 0 < a < 1. The graph of a logarithmic function is a curve that approaches the y-axis as x approaches positive infinity and decreases without bound as x approaches zero from the right.
Applications of Exponential and Logarithmic Functions
Exponential and logarithmic functions have a wide range of applications in various fields. Some of the most common applications include:
