Nucleophilic substitution on alcohols

Exercise 1

It has been found that the nucleophilic substitution of the tertiary alcohols (eg 2-methylpropan-2-ol) by hydrogen halides (eg. $ HBr$) has a carbocation (cation with $+$ charge on $C $) intermediary. 1) Propose a mechanism! 2) Explain the formation of the carbocation!

1) 2) The carbocation is stabilized by the $+I$ effect of the three alkyl groups.