Final Jeopardy
On Monday August 1st Tom purchased 4 baseball cards and Mike purchased 1 baseball card. On Tuesday Tom purchased twice as many baseball cards as he did Monday and on Wednesday he purchased twice as many baseball cards as he did on Tuesday. This continued for two weeks. Mike purchased 20 more cards on Tuesday than he purchased on Monday, and another 20 more cards on Wednesday than he purchased on Tuesday. This continued for two weeks.
1. Write a recursive rule for Tom and for Mike
2. Write an explicit rule for Tom and for Mike.
3. Who has more baseball cards and on what days of the month?
1. Tom: f(1)=4 , f(n)=f(n-1)x2 Mike: f(1)=1 , f(n)=f(n-1)+20
3. From Monday August 1st to Friday August 5th Mike has more baseball cards. After Friday August 5th Tom has more cards.
Tom: f(n)=4(2)^(n-1) Mike: f(n)=20n-19