Each education provider under this chapter and the adult jail facility shall negotiate and execute a written contract for each school year, or such longer period as may be agreed to, that delineates the manner in which their respective duties and authority will be cooperatively performed and exercised, and any disputes and grievances resolved through mediation , and if necessary, arbitration. Any such contract may provide for the performance of duties by an education provider in addition to those in this chapter, including duties imposed upon the adult jail facility and its agents under RCW 28A.194.050, if supplemental funding is available to fully pay the direct and indirect costs of these additional duties.