(a) The county board of equalization and the board of equalization of any metropolitan government organized and existing pursuant to title 7, chapters 1-3 shall, on June 1 each year, meet and sit in regular session as necessity may require until the equalization has been completed; provided, that in any county having a population of not less than twenty-six thousand (26,000) nor more than twenty-six thousand one hundred (26,100), according to the 1970 federal census or any subsequent federal census, the county legislative body may by resolution or ordinance set an earlier date for such board's initial meeting.

(b)

(1) The board shall not sit longer than:

(A) Six (6) days in counties having a population of ten thousand (10,000) or less, according to the 1970 federal census or any subsequent federal census;

(B) Ten (10) days in counties having a population of over ten thousand (10,000) and under twenty thousand (20,000), according to the 1970 federal census or any subsequent federal census;

(C) Fifteen (15) days in counties having a population of over twenty thousand (20,000) and under thirty-five thousand (35,000), according to the 1970 federal census or any subsequent federal census; and

(D) For a number of days fixed by the respective county legislative bodies, but not in excess of thirty (30) days, in counties having a population of over thirty-five thousand (35,000), according to the 1970 federal census or any subsequent federal census.

(2) The county mayor, when the county legislative body cannot act, may extend the time or may call the board in special session at any time, if in the county mayor's judgment the public welfare requires it.

(c) Any county board of equalization, having jurisdiction over a municipality with a beginning tax due date different from that of the county, shall meet as required by the county legislative body, but at least one (1) month prior to the applicable beginning tax due date.