Step 1: Identify the substrate and expected mechanism.
tert-Butyl bromide is a tertiary alkyl halide. Its three bulky methyl groups block backside attack, ruling out S\(_N\)2. It reacts via S\(_N\)1 (ionisation first).
Step 2: Write the rate law.
S\(_N\)1 is unimolecular -- the slow step involves only the alkyl halide. Rate \(= k[t\text{-BuBr}]\). The concentration of NaOH does not appear.
\[ \boxed{\text{Rate} = k[t\text{-BuBr}]} \]