Understanding Exponential Functions | Exploring Rapid Growth and Decay in Mathematics

Exponential function

An exponential function is a mathematical function in the form of f(x) = a^x, where “a” is a constant and “x” is the variable

An exponential function is a mathematical function in the form of f(x) = a^x, where “a” is a constant and “x” is the variable. The base “a” is usually a positive number greater than 1 but can also be a fraction between 0 and 1. In this function, the variable “x” represents the exponent.

Exponential functions have a unique property where the variable “x” is in the exponent position, resulting in rapid growth or decay as “x” increases or decreases. The value of the function increases exponentially if the base “a” is greater than 1, and it decreases exponentially if the base “a” is between 0 and 1.

The graph of an exponential function depends on the value of the base “a”. If “a” is greater than 1, the graph starts at or near the y-axis and increases rapidly as “x” moves to the right. If “a” is between 0 and 1, the graph starts at or near the y-axis and decreases rapidly as “x” moves to the right.

Exponential functions have various applications in fields such as finance, biology, physics, and computer science. They can model population growth, compound interest, radioactive decay, and many other natural phenomena.

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Understanding Function Composition | Finding f(g(x)) for g(x) = √x and g(x) = √x
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Understanding Rational Functions | Definition, Characteristics, and Simplification

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