Question #5 y(t) Answer: 1.4 1.2 0.8 0.6 0.4 0.2 0 1 0 5 t (sec) A periodic signal has the waveform shown in the figure above, where y(t) for the first cycle is defined as: y(t) =e(1-4) y(t) = e(t-4) 10 B. 0.245 for 0≤t ≤ 4 for 4 t ≤ 8 15 The mean value of y(t) is closest to which of the following ? PLEASE REMEMBER TO SHOW ALL WORK THAT LEADS TO YOUR ANSWER! A. 0.123 C. 0.250 20 25 D. 0.487 E. None of the these

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**Question #5**

A periodic signal has the waveform shown in the figure above, where \( y(t) \) for the first cycle is defined as:

- \( y(t) = e^{(t-4)} \) for \( 0 \leq t \leq 4 \)
- \( y(t) = e^{-(t-4)} \) for \( 4 \leq t \leq 8 \)

The graph displays a periodic waveform with the x-axis labeled as \( t \) (seconds) ranging from 0 to 25, and the y-axis labeled as \( y(t) \) ranging from 0 to 1.4. The waveform exhibits peaks approximately around the times 4 seconds, 12 seconds, and 20 seconds, showing an exponential rise and decay pattern between these peaks.

The mean value of \( y(t) \) is closest to which of the following?

Please remember to show all work that leads to your answer!

**Answer:**

A. 0.123  
B. 0.245  
C. 0.250  
D. 0.487  
E. None of these

(Choice B, 0.245, is circled as the selected answer.)
Transcribed Image Text:**Question #5** A periodic signal has the waveform shown in the figure above, where \( y(t) \) for the first cycle is defined as: - \( y(t) = e^{(t-4)} \) for \( 0 \leq t \leq 4 \) - \( y(t) = e^{-(t-4)} \) for \( 4 \leq t \leq 8 \) The graph displays a periodic waveform with the x-axis labeled as \( t \) (seconds) ranging from 0 to 25, and the y-axis labeled as \( y(t) \) ranging from 0 to 1.4. The waveform exhibits peaks approximately around the times 4 seconds, 12 seconds, and 20 seconds, showing an exponential rise and decay pattern between these peaks. The mean value of \( y(t) \) is closest to which of the following? Please remember to show all work that leads to your answer! **Answer:** A. 0.123 B. 0.245 C. 0.250 D. 0.487 E. None of these (Choice B, 0.245, is circled as the selected answer.)
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