(a) The mayor and governing body of a general-law municipality by ordinance may discontinue an area as a part of the municipality if:
(1) the area consists of at least 10 acres contiguous to the municipality; and
(2) the area:
(A) is uninhabited; or
(B) contains fewer than one occupied residence or business structure for every two acres and fewer than three occupied residences or business structures on any one acre.
(b) On adoption of the ordinance, the mayor shall enter in the minutes or records of the governing body an order discontinuing the area. The area ceases to be a part of the municipality on the date of the entry of the order.