Suppose there is a paper having a thickness = 0.002 cm. Now we fold it into half, it's thickness doubles and becomes 0.004 cm. If we again fold it to half, it's thickness becomes 0.008 cm. Thickness is getting doubled every-time we fold it into half. Now if I want to calculate its thickness exponentially, after I have folded it into, let's say 3 times, is this what we get: $(o.oo2 cm)^{3} = 0.000000008 cm^{3}$ or what? Calculating it exponentially, I am getting a very small number but practically the thickness is increasing. I don't know where I am making a mistake, but I know I am missing something. Help.
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$\begingroup$Since it doubles each time you fold it, you should multiply the thickness by $2^{\mbox{number of foldings}}$. You are mistakenly doing $(thickness)^\mbox{number of foldings}$.
So after, say, three folds, you should have $0.002(2^3) = 0.016$ cm. In general, the thickness will be $(0.002)(2^\mbox{number of folds})$.
$\endgroup$ 1 $\begingroup$[Sorry, misread. This doesn't answer the question, but is worthwhile to look at.]
You should check out Britney Gallivan, a high school student who explained how we can actually fold paper 13 times! The previous belief was that paper couldn't be folded more than 8 times.
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