what do you think about this: 10. Virus problem. Modeling assumption (following the wording): at the start of each hour one computer is manually infected, then during the hour the total infected doubles. Let ???? 0 = 1 a 0 =1. Recurrence: ???? ???? + 1 = 2 ( ???? ???? + 1 ) . a k+1 =2(a k +1). Solve: ???? ???? + 1 = 2 ???? ???? + 2 a k+1 =2a k +2. The general solution is ???? ???? = ???? 2 ???? 2 a k =C2 k 2. Using ???? 0 = 1 a 0 =1 gives ???? = 3 C=3. So ???? ???? = 3 2 ???? 2. a k =32 k 2. After 8 hours ( ???? = 8 k=8): ???? 8 = 3 2 8 2 = 3 256 2 = 768 2 = 766 a 8 =32 8 2=32562=7682=766. (You can check ???? 1 = 4 a 1 =4, ???? 2 = 10 a 2 =10, etc.)