Answer to Question #5211 in Differential Equations for Elsie
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^(x-16) = 2^(-2),
x - 16 = -2,
x = 14.
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