Answer: The correct answer is an [tex]S_N1[/tex] type reaction involving the protonated alcohol as the substrate.
Explanation: [tex]S_N1[/tex] reactions are a type of nucleophilic reactions. These reactions are considered as the unimolecular reactions in which only 1 component is used to determine the rate of the reaction.
This reactions involved the generation of a carbocation as an intermediate.
For the reaction of 2-methyl-2-pentanol and HBr, the intermediate formed is  protonated alcohol which yields the product 2-bromo-2-methylpentane.
Reaction is attached in the image below.
