How Does the Unit Step Function Affect the Time Constant?

[Rombus]

Homework Statement

Find the time constant
$x(t)=4 e^{-4t} u(t)$

Homework Equations

$\tau = \frac{1}{\lambda}$

The Attempt at a Solution

$\tau = \frac{1}{\lambda}= \frac{1}{4} = .25$

I know the unit step is shifting the start of the decay function to zero, but I'm not sure how or if this can affect the time constant. So my question is how does the unit step affect the time constant?

 

[Ray Vickson]

Homework Statement

Find the time constant
$x(t)=4 e^{-4t} u(t)$

Homework Equations

$\tau = \frac{1}{\lambda}$

The Attempt at a Solution

$\tau = \frac{1}{\lambda}= \frac{1}{4} = .25$

I know the unit step is shifting the start of the decay function to zero, but I'm not sure how or if this can affect the time constant. So my question is how does the unit step affect the time constant?

It has no effect. Just recall the definition of time constant.

RGV