Which of these is an exponential function? \( y=2^{x} y=\frac{1}{2} x \)

Exponential functions are defined as functions in which a constant base is raised to a variable exponent. In your options, \( y = 2^x \) is clearly an exponential function because the base (2) is constant and the exponent (x) is variable. On the other hand, \( y = \frac{1}{2} x \) represents a linear function, as it can be rewritten in the form \( y = mx + b \), where m and b are constants. To solidify your understanding, think of exponential functions as those fantastic growth phenomena, like how money multiplies in a savings account with compound interest! Meanwhile, linear functions are the steady climb, akin to that treadmill workout that keeps your pace the same.