The solvolysis product of 1-bromo-2,2-dimethylbutane with ethanol initially forms the expected cation but does not give any of the expected 1-ethoxy-2,2-dimethylbutane. Draw the rearranged cation that will eventually lead to the product. Interactive 3D display mode

See image attached and explanation

Explanation:

I have attached a detailed mechanism of the reaction to this answer. This reaction occurs by SN1 mechanism. It implies that the transition state involves a carbocation.

However, the initial carbocation formed is a primary carbacation. Remember that the order of stability of carbocations is methyl< primary < secondary< tertiary. This means that tertiary carbocations are the most stable carbocations. Tertiary carbocations are those in which the carbon atom bearing the carbon atom is attached to three other carbon atoms.

In the mechanism below, the substrate converts from a primary to a tertiary cabocation (most stable) by a 1,2-alkyl shift as shown giving the 3-ethoxy-3-methylpentane product.