Step 1: Identify the reaction mechanism.
Alkaline hydrolysis of tertiary butyl bromide follows an \(\mathrm{S_N1}\) mechanism.
Step 2: Rate-determining step.
The first step involves the ionisation of tertiary butyl bromide to form a carbocation.
This step is slow and requires maximum activation energy.
Step 3: Energy profile interpretation.
The highest peak in an energy profile corresponds to the transition state of the rate-determining step.
Step 4: Conclusion.
Thus, the highest peak represents the transition state of the first step.