The equation x = e^y represents an exponential function where e is the base of natural logarithms, approximately equal to 2.71828. In this equation, y is the exponent, and as y increases, x grows rapidly. This relationship is fundamental in mathematics, particularly in calculus and growth models. In this context, e^y can be interpreted as the amount of growth or decay in various applications, such as population dynamics or finance. The inverse of this function is y = \ln(x) , where \ln denotes the natural logarithm, allowing for the conversion between exponential and logarithmic forms.