Chapter 4 - Functions |
| Functions - Exponential Functions - Contents |
The exponential function has the form y equals e to the power of x. This special equation is the inverse function of the natural logarithmic function. There are other general exponential functions that have the form y equals n to the power of x, where the base number n is a numeric constant, for instance, two to the power of x. These functions are similar to the power function. If it is not specified the exponential function refers to the equation using the special number e as a base number. If n is a common fraction then the numerator is taken to the power and the denominator is taken to the power. The domain of the exponential function is the set of all real numbers. The number n is normally a positive number and then the range of the function is restricted to positive numbers, since all powers of a positive number are positive.
| Functions - Exponential Functions - Examples |
The exponential function:
y = e to the power of x,
when x = 1 then y = e.The natural logarithm is the inverse function:
y = ln(x),
when x = e then y = 1.
| Functions - Exponential Functions - Mysteries |
Math Mysteries: The exponential function increases so rapidly that when something multiplies fast it is said to be increasing exponentially. If y equals two to the power of x, as x increases incrementally from one, y is equal to 2, 4, 8, 16, 32, 64, 128, 256 512, 1024 . . . These numbers may be recognized from the binary system used in computers.
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