Find the \(z\)-transforms of the number sequences generated by sampling the following time functions every \(T\) seconds, beginning at \(t=0\). Express these transforms in closed form.

(a) \(e(t)=\varepsilon^{-a t}\)

(b) \(e(t)=\varepsilon^{-(t-T)} u(t-T)\)

(c) \(e(t)=\varepsilon^{-(t-5 T)} u(t-5 T)\)