Fill in the blank with a suitable preposition.
A preposition is a word which comes before a noun or a pronoun and establishes a relationship between the elements of a clause or words. Option C, "by", is the correct answer as it indicates that something (band's popularity) increases (day by day).
The other options are wrong as at, of, and with indicate a specific location, possession, and inclusion respectively. These uses don't fit in the given question.