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A while ago I read an article on Cracked.com about why you wouldn't want to be immortal. Among many other reasons was that time would speed up for you after so many years and it would make every second seem fleeting. Relative to a year old, each day is a long time because it's a large portion of their life, but to someone who has lived 100 years, it's a very small fraction.

How though, would you calculate what true percentage a certain amount of time is of someone's life? For example, what percent of a two-day-old's life is day one? Day two?

I have no clue what to tag this, but I'm hoping someone who knows what this kind of mathematics is called can retag it.

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I've retagged it algebra-precalculus. It certainly had nothing to do with (what mathematicians understand by) partitions. –  Gerry Myerson Jan 16 '12 at 6:03
    
@GerryMyerson, Alright, thanks. –  mowwwalker Jan 16 '12 at 6:08

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Let's say you've lived for $n$ days in total. Then the portion of your live that the day you just lived took up is $1 / n$.

For example, for a two day old baby you have $n=2$, and so that day they just lived represents $1/2=0.5$ of their life, i.e. half.

For a hundred year old adult, they have lived $100\times 365=36500$ days, so the day they just lived represents $1/36500=.000027$ of their life. Multiplying by 100 to give a percentage nets you $0.0027\%$, which still seems pretty tiny.

More generally, if you've lived for $n$ days then the proportion of your life that the last $m$ days took up is $m/n$.

For example, say you have a two week old baby and you want to know what portion of their life the last hour represents. Then $n=14$ (since they are 14 days old) and $m=1/24$ (since there are 24 hours in the day) which means that the last hour represents

$$\frac{1/24}{14} = \frac{1}{24\times 14} = \frac{1}{336} = 0.0029$$

so the last hour represented about $0.29\%$ of their life.

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