Skewing "a" AND the base
Some time ago on Yahoo's message board for HNP, WHB showed that the growth of CHCL's herd of goats could be represented by an exponential algebraic-expression.
If "n" is the number of years since the first generation reached sexual maturity and "a" is the average age of harvest, then the exponent would be (n - (n - a)) when (n - a) is greater than zero.. But WHB said that "a" should be skewed to reflect the fact that males are probably harvested sooner than females.
To illustrate, suppose male goats are processed at age 3 while females are done at age 10. After the third year, the percentage of females in the herd gets progressively larger as does "a".
WHB thought that the base of the exponent should be close to 2. Another poster suggested 1.7 at the beginning. After more thought, WHB believes that the base should also be skewed higher over time reflecting the logic above.
What it all means is that the growth-rate in the size of CHCL's herd will likely accelerate as time goes by. However, CHCL must plan to decelerate the herd's numerical growth at some distant point due to a finite supply of hay and the market's demand-limit. In other words, the rate of harvest will then begin to accelerate until a desirable equilibrium is achieved.
Finally, WHB figures that there should be a way to derive skewing functions. So the herd's size in year "n" would be given by the skewed base-function to the exponent (n - (n - skewed "a"-function) all times the starting size of the herd. As noted in the HNP post, CHCL can and is using "biotech" methods to considerably bolster the starting size.
This math shows what could happen, not what will necessarily or inevitably result.
