In an arms race between two superpowers, each nation takes stock of its own and its enemy's nuclear arsenal each year. Each nation has the policy of dismantling a certain percentage of its stockpile each year and adding that same percentage of its competitor's stockpile. Nation A dismantles 20%, and nation B dismantles 10%. Suppose that the current stockpiles of nations A and B are 10,000 and 7000 weapons, respectively.
(a) What will the stockpiles be in each of the next two years?
(b) What were the stockpiles in each of the preceding two years?
(c) Show that the "missile gap" between the superpowers decreases by 30% each year under these policies. Show that the total number of weapons decreases each year if nation A begins with the most weapons, and the total number of weapons increases if nation B begins with the most weapons.