i) The differential rate equation.
rate =−d[A]dt=−d[B]dt=k[A][B]2
ii) The rate of the reaction is quadrapued on increasing the concentration of B by two times.
r=k[A][B]2.....(1)
r′=k[A][2B]2
r′=k[A]×4[B]2
r′=4×k[A][B]2......(2)
Substitute equation (1) in equation (2)
r′=4×r