Well I had to look for this a while, but here it is. If you have the time you can double check it, but I am sure it is accurate.
Assume that the earth had an initial population of 2 people, ready to assume their responsibilities as husband and wife and then as parents. Assume also that the average number of children per family (growing to maturity and marriage) was 2 c, with c boys and c girls. In the first succeeding generation, then, there would have been c families (and 2 c individuals, plus the first 2 still living). The second generation, on the same basis, would contain c times 2 c, or 2 c2, individuals. In the third generation, there would be 2 c3 individuals, and so on. The total number of individuals in the world at the end of n generations, assuming no deaths, could be calculated as:
Sn = 2 + 2 c + 2 c2 + 2 c3 + .. - + 2cn, Eqn. 1.
The sum, Sn, can be calculated directly. Multiply both sides of equation (1) by c:
Sn© = 2 c + 2 c2 + 2 c3 + 2 c4 . . . + 2 cn + 2 c(n+1)
Subtracting the first equation from the above:
Sn© - Sn = 2 c(n+1) - 2,
or Sn(c - 1) = 2 c(n+1) - 2
Dividing through by (c - 1) yields the sum Sn as:
Sn = 2 c(n+1) - 2 / (c-1)
Thus,
Sn = 2 [c(n+l) - 1] / (c -1), Eqn. 2.
However, the number of people represented by Sn would have to be reduced by the number who had died since the first generation in order to get the actual population. Now, let the average life-span be represented by x generations. The people who had already died by the time of the nth generation, therefore, would be those who were in the (n-x)th generation, or earlier. This number is:
S(n-x) = 2 [c(n-x+1) - 1] / (c- 1)
The total population at the nth generation, then, combining equations 2 and 3, becomes:
Pn = So - S(n-x) = 2 [c(n+1) - c(n-x+l)] / (c - 1)
Thus,
Pn = 2 [c(n-x + 1)] [cx - 1) / (c-1), Eqn. 4.
Equation 4, in summary, will give the world population n generations after the first family, for an average life-span of x generation,, and an average number of children growing to maturity and marriage of 2c per family. The equation clearly demonstrates how rapidly populations can grow under favorable conditions.
For example, assume that c = 2 and x = 2, which is equivalent to saying that the average family has 4 children who later have families of their own, and that each set of parents lives to see all their own grandchildren. For these conditions, which are not at all unreasonable Table 8 indicates the population at the end of the indicated number of generations, as calculated by equation 4:
TABLE 8. Extended Population Calculation for 6-member Family
Generations Population
5 96
10 3,070
15 98,300
20 3,150,000
30 3,220,000,000
This last number is almost equal to the present world population, so that only 30 generations under these conditions would suffice to produce a population almost equal to that in the world today. The population at 31 generations would be 6.5 billion.
The next obvious question is: How long is a generation? Again, reasonable assumption is that the average marriage occurs at age 20 and that the 4 children have been born by age 35. Then the grand children will have been born by the time the parents have lived the allotted span of 70 years. A generation thus is about 35 years. Ma consider a generation to be only 30 years.
This would mean that practically the entire present world population could have been produced in approximately 30 x 35, or 1050 years!
http://www.ldolphin.org/morris.html[right][snapback]62980[/snapback][/right]
cornelius,perhaps you where not aware,but we havegone from 2 bilion to over 6 billion in less then 100 years.this makes your calculation wortlhless, as well as ignoring plague,famine and such.your calculation is not realistic.
just the fact that in a total of the last 200 years,we would have gone from 1 billion to over 6 billion.and this includes massive famine and death.where do you get your calculations from?no mean of insult here,but you need to look it up again.you need include death ratio for example.your entire calculation seems ot be based on using the current world figures and trying to make it match,i could use 10billion people and make a similar calculation to agree with me.
so i think you havent thought this through cornelius,maybe u used other peoples callculations,but that one does not work,sorry.but its interesting to know how you guys think,unfortunately is just flawed.