The expression e^x - 1 represents a mathematical function where e is the base of the natural logarithm, approximately equal to 2.71828. This function is commonly used in calculus and exponential growth models. When x is zero, the expression equals zero, making it useful for analyzing changes around that point. As x increases, e^x - 1 grows rapidly, reflecting the nature of exponential functions. This function is often encountered in various fields, including finance, physics, and engineering, where it helps describe phenomena such as compound interest and population growth.