## Fermi Questions C

astroblue
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Division: C
State: WA

### Re: Fermi Questions C

Another interesting problem from our regional's test, it's actually not too hard:
If you put 1 cent in a savings account, and it doubles every week, how many pennies will you have at the end of a year?

Schrodingerscat
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Joined: March 2nd, 2011, 7:10 pm
State: KS
Location: Kansas City metro

### Re: Fermi Questions C

Another interesting problem from our regional's test, it's actually not too hard:
If you put 1 cent in a savings account, and it doubles every week, how many pennies will you have at the end of a year?
That one is some exponential math with a little to memorize. 2^52=10^x, log(2^52)=log(10^x), 52log(2)=xlog(10), 52log(2)=x. If you just remember that log(2) is about 0.3, you can find that x is 15.6, thus your power is 16. However, this is also where the flaw of rounding up at 5 and not sqrt(10) appears, as 10^15.6 is 4*10^15 and would be Fermi answer 15.

2win
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### Re: Fermi Questions C

4 days before competition, I've been thrown in. So... besides lots of constants to be memorized, what else should be on my list of things to do?
k-tx. retiring from scioly.

Phenylethylamine
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Location: Harvard University

### Re: Fermi Questions C

4 days before competition, I've been thrown in. So... besides lots of constants to be memorized, what else should be on my list of things to do?
Get used to the idea of what is reasonable.

For example: if your final answer is supposed to be the mass of the moon in kg, and you're getting 2 or 3, is it really reasonable that the moon's mass would be the same order of magnitude as that of a human or a car? If you're trying to calculate the number of cells and the number of atoms in the human body, and you're getting that the answer for atoms is only one more than the answer for cells, is it really reasonable that each cell in the human body only contains ten atoms?

Don't just put down numbers blindly because your calculation turned them out; try to think, "Okay, what else would that be the size of, and is it reasonable that these two things could be about the same size?"
Protein Modeling Event Supervisor 2015
MIT Invitational Tournament
--
Ward Melville High School Science Olympiad 2010-2012
Paul J Gelinas JHS Science Olympiad 2007-2009

nejanimb
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Joined: November 14th, 2008, 5:17 am
State: PA

### Re: Fermi Questions C

If anyone wants a practice test, I wrote the test for the Virginia State tournament, and I've gotten permission to release it.

http://cl.ly/3X2w3b3W0v042q0T3v2r

Let me know what y'all think. Hope it helps in your preparation.
Harriton '10, UVA '14
Event Supervisor in MA (prev. VA and NorCal)

JustDroobles
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Location: WI

### Re: Fermi Questions C

Can you post an answer key as well?

nejanimb
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State: PA

### Re: Fermi Questions C

Sure. PM me.
Harriton '10, UVA '14
Event Supervisor in MA (prev. VA and NorCal)

quizbowl
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Location: Syosset High, WLI, NY --> UChicago '16

### Re: Fermi Questions C

I laughed when I saw today's XKCD article...I miss fermi already :[
2010: 5th in NYS
2011: 4th in NYS
2012: 3rd in NYS
<quizbowl> ey kid ya want some shortbread
<EASTstroudsburg13> I don't know why, but I just can't bring myself to delete this post.