Laplace II: Steps, Impulses & Convolution · Challenge problem

A linear system at rest has unit step response $g(t)=1-e^{-2t}$. Using the impulse response and a convolution, find its response at $t=1$ to the input $f(t)=e^{-2t}$ (applied from $t=0$, system initially at rest). Give an exact answer.