Let's revisit a problem from almost two weeks ago:
If I work on a quality control line at the Zenobia Nut Company, and I routinely eliminate 10% of the nuts which pass me by because they (presumably) don't meet my exacting nut standards, 90% of the nuts will be left over. If a certain practical joker at the company knows that I routinely cull 10% of any given batch of nuts simply because of my unmedicated Obsessive-Compulsive Disorder, and he keeps re-cycling the remaining nuts by me for my inspection/ selection process time after time, how many passes (including the first) will it take for me to have eliminated 30% of the original batch of nuts? Remember: on the second pass, the total batch is only 90% of the size of the original batch.
This problem is the opposite side of the compound interest coin. In compounding, the "base" principal at the beginning of each successive period is increased. In dealing with our nuts, each time we see a batch, it is smaller than the one which preceded it...disturbingly, although I keep consistently eliminating 10% of the nuts on each pass, the initial amount keeps getting reduced so the amount of nuts which I actually toss away keeps getting reduced, as well. This phenomenon is called the "declining balance effect". Every time I go through this process, I am having a decreasing effect on reducing the amount of nuts. In fact, if I carried this process on indefinitely, I would never actually wind up at zero (i.e., nutless).
By way of example: I start with 1,000 nuts, and I want to get down to 700 nuts (70% of the starting amount). Sadly, I cannot simply get rid of 100 nuts (10% of the original amount) at each pass, which would get us down to 700 in exactly three passes. The number of passes will have to be greater than three. Please view the table (and the rest of this article) by clicking on:
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