Presumably "if a quantity is 4 times the size of its base" means a previous measurement of something was made and now the measurement is 4 times the previous one. In that case...
(1) The new measurement is 400% OF the old measurement;
and
(2) The new measurement represents a 300% INCREASE over the old measurement.
So the answer to your question is PROBABLY either 300% or 400%... unless what you mean by "percent rate" is yet something different.