Does Acetate Cause Major E2 On Tertiary Haloalkanes?

This question really confuses me. I've narrowed it down to E2 being favored in step one (giving 2-methylpropene), but I don't see how a relatively weak base like acetate could cause E2 to be the major product. The only other explanation I could think of is that E2 is a substantial minority product, so the reaction isn't synthetically useful. Am I on the right track? Thanks!
[![Acetate and 2-bromo-2-methylpropane](https://i.stack.imgur.com/9qxec.png)](https://i.stack.imgur.com/9qxec.png)


