Question 1099172
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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