While walking along a beach, you notice a fish trapped in a small pool. You release the fish into the ocean, but before it swims away, it turns to reward you for your good deed.

It tells you, "Thank you for freeing me from that tide pool! I was getting claustrophobic. You can choose one of these purses as a reward. You cannot add money to the purses and once you take any money out, the magic is broken and no more money will be added, but you may keep what is inside."

• Purse A which contains $1,000 today. If you leave it alone, it will contain $1,200 tomorrow (by magic). The next day, it will have $1,400. This pattern of $200 additional dollars per day will continue.
• Purse B which contains 1 penny today. Leave that penny in there, because tomorrow it will (magically) turn into 2 pennies. The next day, there will be 4 pennies. The amount in the purse will continue to double each day.

Complete the table for the amount of money in each purse for the given number of days after the fish offers the purses. Be prepared to explain your reasoning for each value.

Here are graphs showing how the amount of money in the purses changes. Remember Purse A starts with $1,000 and grows by $200 each day. Purse B starts with $0.01 and doubles each day. Point P has the coordinates , and point Q has the coordinates .

Graph of two functions, origin O. Horizontal axis, number of days, scale 0 to 25, by 1’s Vertical axis, amount in dollars, scale 0 to 40,000, by 10,000’s. The functions are discrete. Purse A is red and has these points: (0 comma 1,000), (1 comma 800), (2 comma 1,400), (3 comma 1,600), (4 comma 1,800), (5 comma 2,000), (6 comma 2,200), (7 comma 2,400), (8 comma 2,600), (9 comma 2,800), (10 comma 3,000), (11 comma 3,200), (12 comma 3,400), (13 comma 3,600), (14 comma 3,800), (15 comma 4,000), (16 comma 4,200), (17 comma 4,400), (18 comma 4,600), (19 comma 4,800), (20 comma 12 point 2), (21 comma 5,200), (22 comma 5,400), (23 comma 5,600), (24 comma 5,800), (25 comma 6,000), (26 comma 6,200), (27 comma 6,400) and (28 comma 6,600). Purse B is blue and has these points: (0 comma point zero 1), (1 comma point zero 2), (2 comma point zero 4), (3 comma point zero 8), (4 comma point 16), (5 comma point 32), (6 comma point 64), (7 comma 1 point 28 ), (8 comma 2 point 56), (9 comma 5 point 12), (10 comma 10 point 24), (11 comma 20 point 48), (12 comma 40 point 96), (13 comma 81 point 92), (14 comma 163 point 84), (15 comma 327 point 68), (16 comma 655 point 36), (17 comma 1,310 point 72), (18 comma 2,621 point 44), (19 comma 5,242 point 88), (20 comma 10,485 point 76), (21 comma 20,971 point 52).  

1. Which graph shows the amount of money in Purse A? Which graph shows the amount of money in Purse B? Explain how you know.
2. Points and are labeled on the graph. Explain what they mean in terms of the fish's offer.
3. What are the coordinates of the vertical intercept for each graph? Explain how you know.
4. When does Purse B become a better choice than Purse A? Explain your reasoning.
5. Knowing what you know now, which purse would you choose? Explain your reasoning.