I don't have a citation from a prestigious educational institution, but I've seen numerous references to caffeine having a half-life of approximately four hours in the human body. That would fit for the first four hours (13*4=52%), but after that, your formula doesn't fit with the half-life claim (at a flat 13% per hour, you'd be rid of it after 7.6 hours). With a four-hour half-life, after eight hours, your body still has 25% of the original caffeine level left.

Unless you mean that it's a logarithmic scale wherein each hour your body eliminates 13% of what's remaining, in which case, it's closer to the half-life idea (8 hours later, you'd have 32% of caffeine remaining).