In a reaction, $A + B \rightarrow Product$, 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, rate law for the reaction can be written as

Question

( A ) $Rate\; k[A]^2 [B]$
( B ) $Rate = k[A]^2 [B]^2$
( C ) $Rate = k[A][B]^2$
( D ) Rate = k[A][B]