One hundred or more registered voters in any county airport district may make, sign and file a petition with the board of county commissioners asking that thereafter the airport district be governed by a board of airport district commissioners. Within ten days after receipt of such petition, the board of county commissioners shall check the petition. If the petition be found adequate and to be signed by the prescribed number of legal voters, the board of county commissioners shall within a reasonable time call a public hearing, notice of which shall be given by publication one week in advance thereof in a newspaper circulating within the district, at which arguments shall be heard for or against the proposal and if it shall appear to the county commissioners that the residents of the district so desire they shall enter an order declaring that the county airport district shall be governed by a board of three airport district commissioners.