Final answer:
Option D. f(x) = e^-x is an exponential decay function because as x increases, the function value decreases exponentially, which is a critical feature of exponential decay.
Step-by-step explanation:
An exponential decay function is characterized by a decrease over time that can be described by an exponential function, where the original amount decreases by a consistent percentage over a fixed time period. Given the options, D. f(x) = e−x is the correct choice for an exponential decay function. This is because it involves the natural exponential function with a negative exponent, indicating that as x increases, f(x) will decrease, which is a fundamental property of decay. In contrast, A. f(x) = x2 represents a quadratic function that grows with increasing x, B. f(x) = ex is an exponential growth function, and C. f(x) = 1/x is the equation of a hyperbola, which also does not represent exponential decay.