Rate determining step for parallel reaction?
Let's suppose that $\ce{A -&gt; C}$ is the fast step in the parallel reaction scheme.  This implies that $k_2 \gg k_1$.  Thus, $k_1 + k_2 \approx k_2$, it is therefore (approximately) true to write the rate of consumption of $\ce{A}$ as $A_0 e^{-k_2t}$.  This is what is meant by the fast reaction "controlling" rate for parallel reactions.