Fermi Questions C

[astroblue]

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]

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]

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?

[Phenylethylamine]

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?"

[nejanimb]

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.

[JustDroobles]

Can you post an answer key as well?

[nejanimb]

Sure. PM me.

[quizbowl]

I laughed when I saw today's XKCD article...I miss fermi already :[