If a majority of the votes in an election under this subchapter favor the expansion proposition:
(1) the district, by resolution, shall assume:
(A) the duty to serve the designated area of Randall County; and
(B) the responsibility of Randall County to provide medical and hospital care to the indigent and needy inhabitants of that area; and
(2) the Randall County Commissioners Court shall impose a tax sufficient to pay the costs, as determined by the board, of providing medical and hospital care to the indigent and needy residents of that area.