Consider the following problem. Mike and Tim are looking to earn a little extra money. The beach committee offers them the opportunity off picking up plastic bottles, paying them $0.20 per bottle. Mike realizes as they pick up it will get harder and harder to find more bottles. So as an incentive to keep looking he suggest a different form of payment. He suggests $0.10 for the first bottle, and increase the pay by 2% for each bottle after that. Tim thinks Mike is crazy to propose an increase of just 2% per piece. He plans to ask for a one-cent increase for every piece, starting at 15 cents for the first bottle. Suppose the committee accepts each offer.
Answer the following in detail:
- For Mike and Tim, write the first 5 terms of a sequence for payment scheme for each piece of paper.
- Write a function to generate the n-th sequence values (bottle payment) for each Mike and Tim. Explain why you chose that function.
- Using the formula how much will each receive for the 50th bottle? For the 100th bottle?
- Determine the type of sequences for both Mike and Tim.
- Who do you think fairs better in the long term? Explain.