His/Her half-life?

For this question, we know that the half-life of a particular reactant, $A$ is given by $t_{1/2} = \frac{ln2}{k}$ , for $Rate = k[A]$ However, do note that this only applies for a first-order reaction, and hence, cannot be applied directly.

Consider this : $Rate = k[A][B]^2[C]^3$

= $Rate = k[C]^3[B]^2[A]$

= $Rate = k'[A]$ , where $k' = k[C]^3[B]^2$

Hence, the half-life for $A$ is given by $t_{1/2} = \frac{ln2}{k'}$ , which simplifies to

$t_{1/2} = \frac{ln2}{k[C]^3[B]^2}$

With that, for doubling $[B]$ while halving $[C]$ , the overall change in the denominator is that it is half of the original. Hence, the $t_{1/2}$ is $\boxed{doubled}$

This form of using $k'$ to substitute reactant concentration is known as a "Pseudo-first-order" reaction.

Note that a change in $[A]$ does NOT affect its own half-life

http://en.wikipedia.org/wiki/Rate_equation