Rudy collects baseball cards, and he currently has 300 cards. Starting tomorrow, he will purchase 1 pack of 15 baseball cards every day, and every pack he purchases will contain 1 card of a member of his brother???s favorite team. Every time Rudy purchases a pack of cards, he will immediately trade the card of the member of his brother???s favorite team to his brother for 3 cards of members of a different team. Which of these recursive formulas produces the sequence that represents the number of baseball cards that Rudy will have at the end of each day, starting today?

Accepted Solution

Answer: The equation to find the number of cards could be:  c = 300 + 17d, where c equals the total number of cards and d represents the number of days.

The 300 value is the starting amount of cards that Rudy has.

The 17 represents the number of cards that he is getting per day. It started at 15 because that is the amount in a pack of cards. However, he trades one to his brother and gets 3 in return.

15 - 1 + 3 = 17 extra cards per day