given an impulse response h(t) and input x(t) - calculate output

[ovikanobi]

This is in regards to a solved example in my textbook. I am having a difficulty understanding a particular detail. First, some background to explain symbols and processes in this just to level the field. So, in the process of a manual solution of a continuous-time convolution, one is required to identify ranges/intervals of input x(t) (or h(t) ) where the product [MATH]\omega_t(\tau)=x(\tau)h(t-\tau)[/MATH] is true for the entire interval/region. This product, hopefully, is a closed-form equation that would then need to be integrated to arrive at the intermediate result for that interval. So far the leveling of the field. The particular problem is to find y(t) for [MATH]x(t)=u(t)[/MATH] and [MATH]h(t)=e^{-t}u(t)[/MATH] where [MATH]u(t)[/MATH] is the standard step function [MATH]u(t\ge0)=1, 0 [/MATH] elsewhere. The textbook says [MATH]\omega_t(\tau)=e^{-2(t+1)}e^{3\tau}[/MATH] for the sub-interval [MATH]-\infty < \tau < t+1[/MATH] and 0 elsewhere in that interval. My question is in regards to the exponent [MATH]3\tau[/MATH]. Where was this derived from? how?