For the reaction $A+B\to \text{products}$, it is observed that:(a) doubling the initial concentration of $A$ only, doubles the rate.(b) doubling the initial concentrations of both $A$ and $B$, there is a change by a factor of $8$ in the rate.The rate of this reaction is:

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