The unit impulse response of a linear time-invariant system is the unit step function $u(t)$. For $t>0$, the response of the system to an excitation $e^{-a t} u(t), a>0$ will be
- $a e^{-a t}$
- $(1 / a)\left(1-e^{-a t}\right)$
- $a\left(1-e^{-a t}\right)$
- $1-e^{-a t}$