There may be created a board of zoning appeals of a city of the primary class comprised of five members appointed by the mayor and confirmed by the city council, which board shall have power to hear and decide appeals from any decision or order of the building inspector or other officers charged with the enforcement of zoning ordinances in those cases when it is alleged that such decision or order is in error. The board shall also have power to decide upon petitions for variances and, subject to such standards and procedures as the city council may provide in zoning ordinances, to vary the strict application of sign regulations or height, area, parking, or density requirements to the extent necessary to permit the owner a reasonable use of his or her land in those specific instances when there are peculiar, exceptional, and unusual circumstances in connection with a specific parcel of land, which circumstances are not generally found within the locality or neighborhood concerned. The board may also have such related duties as the mayor or city council may assign. The city council may provide for appeals from a decision of the board.