Answer
Rate law is given as:
Rate = $k[(CH_3)_3COH][H^+]$
Work Step by Step
Since the reaction rate doubles when concentration of $H^+$ is doubled, the reaction is first order with respect to $H^+$. Also, the reaction rate is tripled when the concentration of $(CH_3)_3COH$ is tripled. So, the reaction is first order with respect to $(CH_3)_3COH$. Since the reaction rate is unaffected when the concentration of $Cl^-$ is quadrupled, it is zeroth order with respect to $Cl^-$. Hence, the rate law is given as:
Rate = $k[(CH_3)_3COH][H^+]$
