While at a carnival, you notice that one of the stands has the best stuffed bear. You want this bear. The bear, however, can only be acquired for 4650 points. You ask the person working the stand how to get points; they respond that you can redeem tickets at the ticket stand for points. The person working the ticket stand informs you that the more tickets you redeem at once, the more points you will get. If you redeem T tickets, they will give you 5T (T − 1) points. (Encouraging carnival-goers to save up tickets before redeeming saves them a lot of work.)
1.1. The number of points P you receive for your tickets is given by the function P = f(T). Write out f(T), and find f(3) and f(4).
1.2. How many tickets will you have to redeem to get the bear? (Assuming you redeem all of the tickets at once.)