Solution: By the concavity of the function, the point $(a, b)$ cannot be above the curve $y = e ^ { x }$. Since $y = 0$ is an asymptote, the point lies between the curve and the asymptote, so $0 < b < e ^ { a }$. The answer is $D$.
\section*{7. D}
Solution: By the concavity of the function, the point $(a, b)$ cannot be above the curve $y = e ^ { x }$. Since $y = 0$ is an asymptote, the point lies between the curve and the asymptote, so $0 < b < e ^ { a }$. The answer is $D$.