The unit step response of a system is given by (1

The unit step response of a system is given by (1 – e^ατ) u(t), the impulse response is given by—

Given, that unit step response of system
y(t) = (1 – e^{– αt}) u(t).
Let, H(s) is the transfer function of the system.
when x(t)=1

X(s) =	1	, [∵ Laplace transform of x(t)]
	s

and Y(s) =	1	–	1	=	α
	s		s + α		s(s + α)

or Y(s) = H(s). X(s).

	α	= H(s) ·	1
	s(s + α)		s

or H(s) =	α
	s + α

Now, according to question, we have to calculate y(t) for input x(t) = δ(t)
then X(s)= 1

H(s) =	α
	s + α

X(s)=?
Now, Y(s) = X(s).H(s)

or y(s) = 1·	α
	s + α

Taking inverse Laplace transform to calculate y(t)
y(t) = α·e^{– αt} u(t).
Hence, alternative (B) is the correct answer.

	1	e^{– ατ} u(t)
	α