Question

Which of the following functions grows at the same rate as e^x as x goes to infinity?
a) e^(x+3)
b) e^(3x)
c) e^(2x)
d) e^(-x)

Answer 1

e^-x decreases, so it is clearly not a choice.

All the rest have slopes that grow to infinity, and it makes little sense to compare infinities.

Still,
e^(x+3) = e^3 * e^x
e^(2x) = (e^x)^2
e^(3x) = (e^x)^3
of all those, I'd say that e^(x+3) grows most like e^x, but its slope is always e^3 times as much. Poorly worded question. k*∞ = ∞^2 = ∞^3 = ∞.