The names and votes of members shall be recorded on an action taken by the board of county commissioners or by a committee of the board of county commissioners if the action is on an ordinance or the appointment or election of an officer, except the vote for chairperson may be by secret ballot. The vote and the name of the member voting on other questions or motions shall be recorded at the request of 1/5 of the members present if the question or motion is before the board, or 1/3 of the members present if the question or motion is before a committee of the board. A record that is made pursuant to this section shall be available for public inspection.