SOLUTION: 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 $

Question 1099172: 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.
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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
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let n be the number of bottles each picks up. Then:
Mike's bottles: .1 + 0.1*(1.02)^(n-1) represents the total pay for n bottles he picks up (for n>1)
Tim's bottles: (0.15+.01(n-1)) for n bottles that Tim picks up
For Mike, the 50th bottle equals: .1+0.1*(1.02)^49=.1+.26=0.36
For Tim, the 50th bottle is worth: .15+(.01)49=0.64
For Mike, the term is geometric, because the price per bottle rises exponentially, while for Tim the price per bottle rises algebraically, by a constan)t 1 cent per extra bottle. In the long run, Mike is going to make more per bottle.
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