The correct option is C will have been searching
A tense is a form of a verb which provides more details about the verb (time, completion, progress, etc). Option C)will have been searching is correct as it is the correct structure of the future perfect continuous tense. The future perfect continuous tense is used to indicate an action in progress at a specific time(the time we reach) in the future. The other options are wrong as no other tense can be used here. The correct answer is C)will have been searching.