How do we know radioactive decay occurred at the same rate in the past?

Radioactive decay just means the decay is proportional to the amount, or concentration, of the material. If it doesn't change now (the decay constant remains constant) then the constant isn't a function of the concentration (which was implied when I called it a constant, but whatever). So the equation holds, but decay was faster in the past because the concentration, of Carbon-12, for example, was higher.