What is the average power?

0, because finite energy divided by infinite time vanishes

Power and energy of e^(-2t)u(t)

Short answer

Integrate |x(t)|^2 from 0 to ∞: E = ∫ e^{-4t} dt = 0.25 J. Average power P = lim (1/2T)∫ e^{-4t} dt = 0. The signal is an energy signal.

Determine the power and energy for a continuous time signal of x(t) = e^(-2t)u(t) (t ≥ 0).

x(t) = e^(-2t) u(t)

E = ∫ |x(t)|² dt = ∫₀^∞ e^(-4t) dt = [-e^(-4t)/4]₀^∞ = 1/4 = 0.25 J

P = lim (T→∞) (1/2T) ∫_{-T}^{T} |x(t)|² dt = lim (1/2T) · (1/4)(1 - e^(-4T)) = 0

The energy is finite and non-zero, and the average power is zero.

Answer: E = 0.25, P = 0. The signal is an energy signal.

✓ Answer checked by Claude Opus 5.5 (high effort)