Why doesn't this reaction use an E2 mechanism?

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gauss44
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tert-butyl bromide + MeOK in MeOH ----->

I would think that MeOK would dissociate in solution making it MeO- which would be strong enough to yank a proton off tert-butyl bromide and initiate an E2 reaction. Where am I going wrong?

PS - I am a tutor who hasn't done organic chemistry for a while, so please leave this here AND do NOT send me to the ¨Homework¨ section. This is NOT homework.
 
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The central carbon atom in tBut-Br is tertiary, which gives rise to high steric hinderance, which means that we can exclude Sn2, leaving E1, E2 or Sn1. Continuing, if we consider the other reactant Me-OK, it is negatively charged and thus a strong nucleophile/base. However, since it is strong Sn1 or E1 are unlikely to happen, leaving us only E2 to happen. Don't forget though that Sn1, E1 and Sn2 will happen, but it is to a such small extend that it can be approximately unconsidered.