A linear time$-$invariant $($LTI$)$ system has a step response $s(t)=2e^{-3t}*u(t).$

a$)$ Find and sketch the impulse response $h(t)$ of the system.

b$)$ Find and sketch the ramp response $r(t)$ of the system.

c$)$ Find the response of the system to an input $x_1(t)=(t)-5(t-4).$

e$)$ Find the response of the system to an input $x_2(t)=e^{-t}u(t).$