The first$-$order system is applied to the impulse function $($impulse function$)$ as a result of the time$-$dependent function of the variable $()=/.$

a$)$ Determine the initial and time constant of the impulse function of the system.

b$)$ Pay attention to the time$-$dependent function of the variable in the case of increasing the performance of the same$-$sized step instead of the impulse. Y$($t$)=?$