Mike & Tim are looking to earn a little extra moolah. The beach committee offers picking up plastic bottles @ .$20 cents per bottle. Mike realizes that it will get harder and harder to find more bottles as they pick up. So, as an incentive to keep looking Mike suggests a different form of payment. Mike suggests .$10 cents for the first bottle, and to increase the pay by 2% for each bottle thereafter Tim thinks Mike is insane to propose an increase of just 2% per piece. Tim plans to ask for a .$01 cent increase for every piece, starting at $.15 cents for the first bottle. Suppose the committee accepts each offer:
Answer the following:
For Mike and Tim, write the first 5 terms of a sequence for payment scheme for each piece of paper.
How would you generate 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.x