The function e^-x is an exponential decay function, where e is the base of natural logarithms, approximately equal to 2.718. As x increases, the value of e^-x decreases, approaching zero but never actually reaching it. This behavior makes it useful in various fields, including mathematics, physics, and finance. In practical applications, e^-x models processes that decrease over time, such as radioactive decay and cooling of objects. Its graph is a smooth curve that starts at 1 when x = 0 and declines steadily as x increases, illustrating the concept of diminishing returns.