Effect of Concentration on Reaction Rate

A reaction represented by the equation A + 2B → C exhibits first-order kinetics with respect to A and second-order kinetics with respect to B, yielding a rate law of the form: rate = k [A][B]^2. At time t = 0, the initial concentrations of reactants A and B are [A]₀ = 0.1 M and [B]₀ = 0.2 M, respectively. Calculate the rate of the reaction at t = 0, assuming that k = 4 M^-3s^-1.

Given this setup, determine the effect of doubling the concentration of B on the initial rate of reaction, while keeping the concentration of A constant.