Determining the Order of Reaction in Chemical Kinetics

A chemist is studying the reaction between substance A and substance B, which produces products C and D. The reaction is represented by the following equation:

A + B → C + D

The chemist measures the rate of reaction at various concentrations of reactants and finds that doubling the concentration of A increases the rate of reaction by a factor of four, while doubling the concentration of B only doubles the rate. Which of the following statements about the rate law for this reaction is correct?