I've been thinking...
Adults need 7-9 hours of sleep a night, so lets go with 8 as an average.
Most adults drink a cup of coffee in the morning, right? (Limit the subject pool to those who do because people who don't need coffee are freaks and ought to be weeded out of society, or at the very least my group of friends.)
So it's basically 8 hours of sleep and 1 cup of coffee, on a normal day.
8hours:1cup. It follows that 1hour:8cups.
Let x= 8-actual amount of sleep, or the lack of sleep based on an 8 hour sleep requirement.
Then, c=(1+x)(t-1) where c is coffee intake, t is time, and x is the lack of sleep.
If you slept for 7 hours:
the second day it would be c=(2)(1)= 2 cups, because lets be honest, two days of 7 hours would be GLORIOUS.
the third day it would be c=(2)(2)=4 cups.
Originally I had (t-1) as an exponent, but even Koshka the caffeine addict says 16 cups of coffee in one day is unreasonable. There are some other kinks to be worked out. It probably should also be the total amount of coffee you should have, in cups, over the time period, t, but that only works for t>2.
In short, it is totally acceptable for me to have 4 cups of coffee today.
your someone-give-me-a-caffiene-IV-drip-please sister