I attempted to draw a graph of this data, and the line ln(DeathRate)=(31/375)*Age+1.856 happens to agree with the data pretty well for ages 5-14 and 30-84. This confirms "Gompertz's law." I believe it also works well at ages 85-95. However, it does not work at ages <5 and 15-29.
picture: https://dl.dropboxusercontent.com/u/3507527/DeathRates2007USA.png --I made several attempts to produce better laws. My first attempt was an already proposed formula: DeathRate = C + exp(A*Age+B) where I find A=0.071 B=2.626 C=6.09 has maximum |error|<0.308 for the ln(DeathRate) over the CDC 5-year age bins, for all Age>19. But it is no good for ages 0-19. DeathRate = C*Age^Q + exp(A*Age+B) with A=0.0828 B=2.29 C=15.7 Q=-1.88 has maximum |error|<0.469 for the ln(DeathRate) over the CDC age bins, for all integer Age>0. DeathRate = C/Age + Q + exp(A*Age+B) with A=0.0812 B=2.388 C=16.5 Q=-3.81 has maximum |error|<0.455 for the ln(DeathRate) over the CDC age bins, for all integer Age>0. (And I believe this last fit's parameters can be improved further, max |error|<0.450 is definitely achievable.) In the last of these formulae, the Q term stays fixed, the exp(A*Age+B) term increases exponentially with age, and finally the C/Age term decreases with age. The fact Q is negative kind of ruins the interpretation that it represents "acts of God," so I guess it instead represents "self repair" or "medical help" (?), see below. The C/Age term models the effect of "experience" as your brain and/or immune system "learn" to handle threats to your existence -- as time T goes by you learn to handle about T kinds of threats, leaving only a fraction of order 1/T of threats still able to kill you. The exponentially increasing Gompertz term perhaps could be explained as follows. Imagine your life consists of N "answers" for some very large initial value of N. Each year, any particular answer you own, is obliterated with some fixed probability p (all events independent). Also, each year, a random "challenge" is posed to you. You live if you still have the answer to that challenge. In this model, the number of still-existing answers tends to fall exponentially with time, ultimately making it exponentially unlikely you will survive the next challenge. The negative Q could also be regarded as representing a fixed ability to "invent" an answer you do not actually have.