Which of the following explains how to obtain the graph of $y=2+5(1+e^{-x})$ from the graph of $y=e^{-x}$?

(a) Vertically stretch the graph of $y=e^{-x}$ by a factor of 5 and then shift this result up 2 units.
(b) Vertically stretch the graph of $y=e^{-x}$ by a factor of 5 and then shift this result down 2 units.
(c) Vertically stretch the graph of $y=e^{-x}$ by a factor of 5 and then shift this result up 7 units.
(d) Vertically stretch the graph of $y=e^{-x}$ by a factor of 5 and then shift this result down 7 units.