Rewriting a piecewise function using step functions

[selig5560]

TL;DR

Function properties

Suppose we have a piecewise function

f(t) = exp(c*t) when 0 <= t < 2 and f(t) = 0 when t >= 2.

Can the above be rewritten as

f(t)= exp(at)*[H(t-0) - H(t-2)],

H is a heaviside function.

 

[member 587159]

What is $a$?

 

[mathman]

You didn't specify f(t) for t < 0.