Consider the following continuous time signal:

x$($t$)=100$e$^(-500$t$)$ where t$>=0$

Follow a procedure like that in EOCE $8\mathrm{.}8$ and EOCE $8\mathrm{.}7$ to perform the following:

Find the approximate maximum frequency, f$\_($m$),$ where the magnitude spectra approaches

zero magnitude. Justify your work.

Sample x$($t$)$ at f$\_($s$)>2$f$\_($m$)$ and find x$($n$)$

Sample x$($t$)$ at f$\_($s$)<mn>2</mn>$f$\_($m$)$ and find x$($n$)$

Draw a conclusion by observing the plots for the two x$($n$)$ in parts $2$ and $3.$