  The one-dimensional contact process with weak to intermediate quenched
disorder in its transmission rates is investigated via quasi-stationary Monte
Carlo simulation. We address the contested questions of both the nature of
dynamical scaling, conventional or activated, as well as of universality of
critical exponents by employing a scaling analysis of the distribution of
lifetimes and the quasi-stationary density of infection. We find activated
scaling to be the appropriate description for all disorder strengths
considered. Critical exponents are disorder dependent and approach the values
expected for the limit of strong disorder as predicted by strong-disorder
renormalization group analysis of the process. However, even for the strongest
disorder under consideration no strong-disorder exponents are found.
