Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π]...

Equating the equations of the curves $C_1$ and $C_2$:

$e^{-x} = e^{-x}(\sin x + \cos x)$

Since $e^{-x} \neq 0$ for all real $x$, dividing both sides by $e^{-x}$ gives:

$\sin x + \cos x = 1$

Multiplying both sides by $\dfrac{1}{\sqrt{2}}$:

$\dfrac{1}{\sqrt{2}}\sin x + \dfrac{1}{\sqrt{2}}\cos x = \dfrac{1}{\sqrt{2}}$

$\sin\left(x + \dfrac{\pi}{4}\right) = \dfrac{1}{\sqrt{2}}$

The general solution is given by:

$x + \dfrac{\pi}{4} = 2m\pi + \dfrac{\pi}{4}$ or $x + \dfrac{\pi}{4} = 2m\pi + \dfrac{3\pi}{4}$ for integer $m$

This simplifies to:

$x = 2m\pi$ or $x = 2m\pi + \dfrac{\pi}{2}$

Given the interval $x \in [0, 10\pi]$, the valid values for $x$ are:

For $x = 2m\pi$: $x = 0, 2\pi, 4\pi, 6\pi, 8\pi, 10\pi$ (6 solutions)

For $x = 2m\pi + \dfrac{\pi}{2}$: $x = \dfrac{\pi}{2}, \dfrac{5\pi}{2}, \dfrac{9\pi}{2}, \dfrac{13\pi}{2}, \dfrac{17\pi}{2}$ (5 solutions)

The total number of points of intersection is $n = 6 + 5 = 11$.

Answer: $11$