Final answer:
None of the given options is an exponential decay function. An exponential decay function decreases as the independent variable increases and can be represented by the formula f(x) = me^-mx. The closest choice is D. f(x) = 1/x, which is actually a rational function.
Step-by-step explanation:
An exponential decay function is characterized by a decrease in value as the independent variable increases. It can be described by the formula f(x) = me-mx, where m is the decay rate and x is a non-negative value representing the independent variable.
Among the given options, none directly represent this form. However, D. f(x) = 1/x can sometimes be confused with an exponential decay function since it decreases as x increases. But technically, f(x) = 1/x is a rational function, not an exponential decay function.
If we analyzed an exponential decay function with a decay parameter of m = 0.1, the probability density function would be f(x) = 0.1e-0.1x and the cumulative distribution function would be P(X < x) = 1 - e-0.1x for x >= 0. Graphing this would show a rapidly declining curve from left to right, and the area under the curve to the left of a specific point represents the probability of the variable being less than that point's value.