Bacteria in a petrie dish double the area they cover everyday. If the dish is covered after 16 days, on what day was only one quarter of it covered?
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Expert's answer
2011-11-29T08:56:55-0500
Let the area of the whole dish be 1. Suppose the bacteria covered an area S at the beginning. After the first day it covered the area 2S, after the second - 4S and so on. So, after n days the bacteria covered (2^n)*S. We know that after 16 days it covered the dish. We get:
(2^16)*S = 1, S = 1/(2^16) = 2^(-16).
Let x be the number of days that after x days only one quarter was covered. Then
(2^x) * S = 1/4, (2^x) * 2^(-16) = 2^(-2), 2^(x-16) = 2^(-2), x - 16 = -2, x = 14.
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