Answer:
The most consistent mechanism is SN1.
Step-by-step explanation:
The solvolysis of tert-butyl iodide in methanol will arise by the SN1 mechanism.
The reason for that is due the geometric structure of tert-butyl. The tertiary structure allows the formation of a stable carbocation, after the loss of the iodide ion. The carbocation will then be attacked by methanol molecules forming an eter.