Posted 29 August 2005 - 09:49 PM
Heh, mortality rates have fallen at an exponential rate. But, consider the implication of such a statement. People normally think of exponential in terms of things getting bigger and bigger, or faster and faster, of accelerating.
For example, if the mortality rate fell by 2% in the 1950's, and then by a further 3% in 1960's, and then by a further 4.5% in the 1970's, and then by a further 6.8% in the 1980's, and then by a further 10.1% in the 1990's, etc. That would be what is "implied" by exponential.
But what is actually the fact of the matter, is that a mortality rate that declines at a constant, say 5%, relative rate (relative to its previous value) is exponential, but on the "tail" or "decelerating" side of the curve, not the "exploding" or "accelerating" side of the curve.
For example, a mortality rate (for some unspecified mortality class) of 0.50000 in the 1950's, which reduced to 0.47500 in the 1960's, which reduced to 0.45125 in the 1970's, which reduced to 0.42869 in the 1980's, which reduced to 0.40725 in the 1990's, is declining exponentially (on a linear scale: on a logarithmic scale, it's declining linearly). But consider, on a linear, absolute scale, the decline is actually decelerating (since otherwise it could reach zero and overshoot the mark into negative territory, which I guess would involve zombies rising from the dead!).
So rather than get worked up about this, let's just recognize that this was a simple misinterpretation by several parties on what "exponential" implied and/or meant. In such cases, one should be clear and provide explanation, or avoid the term altogether. Even though the use of the word "exponential" was technically correct, in declaring a linearly decelerating drop in mortality rates (i.e. the "tail" side of an exponential curve, like that used in half-life studies), it was rather implicitly saying that the rates were accelerating in some meaningful way. "Exponential" is a very charged word. Let's just stick with decreasing at a near-constant relative rate (or percentage rate, where the percentage implies it's relative) per time.