Is E1 or E2 the Correct Mechanism for Bulky Base Eliminations?

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Zayan
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TL;DR Summary: E1 or E2? I did the E2 hoffman elimination because it's tbuOh so it's bulky hence does E2 with Hoffman as major product so I chose option A. But the solution manual has done E1 reaction and rearrangement so the answer marked is C. What is the correct mechanism?

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The alcohol is bulky and therefore NOT likely to be engaging in E2. Hoffman elimination has a strong base. Is there a strong base in this example?

E1 is favored by a polar,non-nucleophilic solvent like t-Butanol and good leaving groups like I. This is textbook E1.
 
chemisttree said:
The alcohol is bulky and therefore NOT likely to be engaging in E2. Hoffman elimination has a strong base. Is there a strong base in this example?

E1 is favored by a polar,non-nucleophilic solvent like t-Butanol and good leaving groups like I. This is textbook E1.
I had read that bulky bases do hoffman elimination (E2) because of less crowding.