A piece of paper is 0.1 mm thick. When folded, the paper is twice as thick.
Assume that you could fold the paper as many times as you want. How many folds would be required for the paper to be taller than Mount Everest(8850m)?

Question

A piece of paper is 0.1 mm thick. When folded, the paper is twice as thick.
Assume that you could fold the paper as many times as you want. How many folds would be required for the paper to be taller than Mount Everest(8850m)?

anonymous · Answer

solve $$0.1\times 2^x=8850$$

anonymous · Answer

oh that is wrong sorry

anonymous · Answer

what is a mm?  one thousands of a meter?

anonymous · Answer

1m=100cm, 1cm=10mm, so...ya.

anonymous · Answer

so solve $$0.0001\times 2^x=8850$$ first step is to divide by $0.0001$ aka multiply by $10,000$ and get $2^x=88,500,000$

anonymous · Answer

then solve for x either by trial and error or using logs. do you know how to use logs for this?

anonymous · Answer

the log method is to write 
$$x=\frac{\log(88,500,000)}{\log(2)}$$

anonymous · Answer

why would you multiply by .0001? I thought it was just .1 mm, and that you only convert the 8850 to 8850(000). And no, I don't know how to use logs for this...

anonymous · Answer

i get around 27, perhaps a surprisingly small number

anonymous · Answer

ok lets got back to the mm
the height of mt everest  is given in meters, and the width of the paper is given in mm so we have to convert them to the same units otherwise we cannot compute anything

anonymous · Answer

how??? I think I get how you went to the equation you did, but how to go from there?

anonymous · Answer

apparently 1 mm = .001 meters (one thousandth of a meter) and so 0.1 mm = .0001 meters right?

anonymous · Answer

therefore first we want to convert mm to meters
then we know the number of pieces of paper, when folded in half go like this

anonymous · Answer

$2, 4, 8, 16, 32, ...$   i.e..
 $2, 2^2,2^3,2^4,...$

anonymous · Answer

Oh, yeah!!! I was just doing it the other way. converting to mm instead of m. I just realized that...srry

anonymous · Answer

so after "n" folds the number of pieces of paper will be $2^n$

anonymous · Answer

each with width .0001 mm so we want to solve $.0001\times 2^n=8850$ for n

anonymous · Answer

so far so good?

anonymous · Answer

Well, I don't get the part when you are showing the 2, 4, and all the other numbers... where did you get the 2? I s that from doubling? And where did the 0.1 go?

anonymous · Answer

site is crashing on me, so i may not be able to respond, but the idea now is to multiply both sides of the quation by 10000, then see if you can find an $n$ for which $2^n\geq 88,500,000$

anonymous · Answer

yes you are doubling

anonymous · Answer

wait, are you using 0.1 with 88500000?

anonymous · Answer

each time you fold the paper in half you double the number of pieces of paper. as for the .0001 it is still there, i just wrote the numbers $2, 4, 8, 16, 32...$ so you could see that the paper is doubling and after n folds you will have $2^n$ layers, each of which is $.0001 m$ thick, for a total thikness of $.0001\times 2^n$

anonymous · Answer

i got rid of the .1 by conveting it to meters, so now the .1 mm is .0001 m

anonymous · Answer

that is why i wrote $$.0001\times 2^x=8850$$

anonymous · Answer

ya, I get that
(btw, my computer is not exactly the fastest computer on the face of the earth, so if I ask you a question right after you answer it, it is because of the buffering)

anonymous · Answer

So I don't get how to solve the log part...

anonymous · Answer

if you don't knowabout logs yet, then solve by trial and error. see what power you raise 2 to in order to get a number bigger than 88,500,000

anonymous · Answer

oh, I see... So I tried out the logarithm thing on my calculator and I got about 26.402, and I would round that up, right?  And so that would give me 27? But how... I mean, can... you do that logarithm equation by hand?