Average Value of an Exponential Function

Let the function $f$ be defined by $f(x) = e^{-x}$. Consider the following statements regarding the average value of $f$ on the interval $[0, L]$, where $L > 0$.

I. The average value is given by the expression $\frac{1}{L}\int_0^L e^{-x}dx$.

II. The average value is always less than $e^{-L/2}$.

III. As $L$ approaches infinity, the average value approaches 0.

Which of the statements above is/are true?