Question Stem for Question Nos. 15 and 16: Consider the curve C₁ given by y = e⁻ˣ for x ∈ [0, 10π], and the curve C₂ given by y = e⁻ˣ(sin x + cos x) for x ∈ [0, 10π]. Let n be the total number of points of intersection of the curves C₁ and C₂. Suppose that α₁, α₂, …, αₙ ∈ [0, 10π] are the x-coordinates of the points of intersection of the curves C₁ and C₂ such that α₁ < α₂ < ⋯ < αₙ. The value of n is ___________.
For the Question Stem for Question Nos. 15 and 16, let β be the area of the region enclosed between the curves C₁, C₂, and the lines x = α₁ and x = α₄. Then the value of −(1/π) logₑ(β − 2e^(−π/2)) is ___________.