---
title: "Power and energy of e^(-2t)u(t)"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:power-energy-e-2t"
source: https://www.bctengineer.com/q/semester_5/data_communication/power-energy-e-2t
site: BCT Engineering
---

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

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2072 Kartik, 4 marks
- Video: [Energy and Power Signals (Example 6)](https://www.youtube.com/watch?v=T8NZyfzA9No) — EnggClasses
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/power-energy-e-2t
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

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

## 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.

## Answer

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

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

#### Power
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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the energy of e^(-2t)u(t)?
   A. 0.5
   B. 1
   C. Infinity
   D. 0.25
   Answer: D. Integral of e^(-4t) from 0 to infinity is 1/4. (Key point: Energy)

2. In the energy integral, what is integrated?
   A. |x(t)|^2, giving e^(-4t)
   B. x(t), giving e^(-2t)
   C. |x(t)|, giving e^(-2t)
   D. x(t)^3
   Answer: A. Energy is the integral of the squared magnitude. (Key point: Why squared)

3. What is the average power?
   A. 0.25
   B. 0, because finite energy divided by infinite time vanishes
   C. 0.125
   D. Infinity
   Answer: B. The 1/2T factor sends power to zero. (Key point: Power)

4. The signal is classified as
   A. A power signal
   B. Both energy and power signal
   C. An energy signal
   D. Neither
   Answer: C. Finite nonzero energy and zero power. (Key point: Classification)

## Related in Data Communication

- [Energy or power of DT cos(3πk/16)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adt-signal-cos-energy-power) — Data Communication, chapter 2
- [Properties of continuous-time Fourier series](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afourier-series-properties) — Data Communication, chapter 3
- [Energy or power: e^(-a|t|)u(t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-exp-abs) — Data Communication, chapter 2
- [Energy versus power signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-distinguish) — Data Communication, chapter 2, asked 6×
- [Energy or power: unit step, impulse](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-check-signals) — Data Communication, chapter 2, asked 2×
- [Causality, stability; energy and power signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acausality-stability-energy-power) — Data Communication, chapter 2

## Related in other subjects

- [Shannon-Hartley theorem; energy/power of e^(−2t)u(t)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashannon-hartley-energy-e2t) — Communication Systems, chapter 1
- [Energy and power of (3+4j)e^(2t)u(−t)](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aenergy-power-complex-exponential) — Signals and Systems, chapter 1
- [Energy and power signal; bandwidth of a system](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aenergy-power-bandwidth-system) — Communication Systems, chapter 1
- [Power of energy signal is zero](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aenergy-vs-power-signal-example) — Signals and Systems, chapter 1