Exponential Funtion
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 constant “a” is commonly referred to as the base of the exponential function. The base “a” must be a positive number and not equal to 1 in the standard exponential function.
In an exponential function, the variable “x” represents the exponent or power to which the base “a” is raised. As the value of “x” changes, the function will produce different values. The behavior of an exponential function depends on the value of the base “a”.
When the base “a” is greater than 1, the exponential function will exhibit exponential growth. This means that as “x” increases, the function will increase at an accelerating rate. The larger the value of “a”, the steeper the curve of the graph will be.
Conversely, when the base “a” is between 0 and 1, the exponential function will display exponential decay. In this case, as “x” increases, the function will decrease at a decreasing rate. The smaller the value of “a” (but still greater than 0), the more gradual the curve of the graph will be.
Exponential functions have many real-world applications, including population growth, compound interest, radioactive decay, and various natural phenomena. They are extensively used in fields such as finance, biology, physics, and computer science to model and predict exponential growth or decay processes.
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