The producer of a certain commodity determines that to protect profits, the price p should decrease at a rate equal to half the inventory surplus S−D, where S and D are respectively the supply and demand for the commodity. Suppose the supply and demand vary with price in such a way that S(p)=80+3p and D(p)=130−2p and that the price is 5 dollars per unit when t=0. Determine p(t).