(i) $x(t) = 0.9e^{-3t} u(t)$

$E = ∫\limits_{-∞}^∞|x(t) |^2 dt $

$ =∫\limits_{-∞}^∞|0.9e^{-3t} u(t) |^2 dt \\ = 0.81∫\limits_0^∞e^{-6t} dt \\ = 0.81[\dfrac {e^{-6t}}{-6}]^{\infty}_0 \\ = 0.81/6 \\ E= 0.135J$

Since the signal is not periodic hence it’s not a power signal but it is a energy signal.

(ii) $ …