An exponential function that has the natural numbers (positive integers) as its domain and is commonly used is the natural exponential function, which is denoted as:
f(x) = e^x
In this function:
- "e" is the base of the natural logarithm, approximately equal to 2.71828.
- "x" represents the input value, which is a natural number (positive integer).
This function is defined for all positive integer values of "x" and exhibits exponential growth as "x" increases, with the output values increasing rapidly. It's a fundamental function in mathematics and has various applications in fields such as calculus, finance, and science.