In a reaction, $A+B\to \text{Product}$, rate is doubled when the concentration of $B$ is doubled, and rate increases by a factor of $8$ when the concentrations of both the reactants ($A$ and $B$) are doubled. The rate law for the reaction can be written as:

1. A
   $\text{Rate}=k[A{]}^2[B]$
2. B
   $\text{Rate}=k[A][B{]}^2$
3. C
   $\text{Rate}=k[A{]}^2[B{]}^2$
4. D
   $\text{Rate}=k[A][B]$