Can the unit step function express e^t between 0 and 2?

[kasse]

Homework Statement

Express f(t) = e^t, 0<t<2, using the unit step function

2. The attempt at a solution

e^t*u(t-2) is an expression for a graph of the function that is zero until t=2. My guess is

e^t*u(t+2)

 

[Dick]

That's not a very good guess. That makes f(-1)=e^(-1). You want to subtract two step functions so you get something that's only nonzero between 0 and 2.