How 5000 Arab soldiers grew up to 60 million Arains?

We have answer it before but today we will describe it scientifically. After every 25 to 30 years a new generation starts. Example My grand father born in 1928 than my father in 1952 and me born in 1983, my son born in 2012. So, we can easily estimate that four generations exist in a century but chance of error could increase or decrease equally.
Case:
5000 Soldiers got married in Rajpoots and Jatt families with 5000 women.Arabs were like to marry 4 women at a time but we are not going to estimate in that way. We will take one partner for each soldier.
Lets start from 8th century when Arains got established in subcontinent. Average  children ratio in subcontinent was 8/family at that time,  take it as  50% boys  and same ratio of girls,  means there were 4 children of each soldier to continue its chain of generation. Now we can easily estimate  that how many children he produced in a century it will be 1x4x4x4=32 persons in 100 year. lets  assume that half  of them die or martyred  the remaining were 16.
Hence  5000 soldiers produced 80000 persons (5000x16) in 100 years. Next 100years 80000 persons produced (80000x16)=1280000Persons.
In 10th Century Arain population was about 1280000. If we simply apply the growth ratio of 2%/year it will be projected up to (1280000+25600)-10500 Die with the ratio of 8/1000=1295000
In 1001=1295000,
In 1002=1295000+(1295000x2%)=1320900-10567deaths=1310333
In 1003=1310333+(1310333x2%)=1336539-10692 deaths=1325846
Hence 15000 persons added in population every year. After 100 years 1500,000 people added
So, In 1101 Arain Population was 2795000.
In 1101=2795000+(2795000x2%)=2850900-22807deaths=2828092
In 1102=2828092+(2828092x2%)=2884654-23077deaths=2861577
Hence in 11th century  33000persons added in population per year. After 100 years 3300,000 people added in population of Arains. Total population in 1201 was 6095000.
In 1201=6095000+(6095000x2%)=6216900-49735=6167165.
In 1201=6167165+(6167165x2%)=6290508-50324=6240184.
In 12th Century 72500 people added in population every year, after 100 years 7250000 people added in population of Arains. So they became 13345,000.
Now we can easily follow the trend shown in above calculation. There is a trend of 220% increase in grew population of every year's population after every 100 years. So, we can easily increase 220% of 72500 and can calculate population next 100 years. 72500x220%= 159500 growth per year in 12th century. So, 15950000 people added in population. Total population in 1301=13345000+15950000=29295000
We can make it more easy by multiplying 220% with next 7 centuries (220%x7)=1540%
Finally we can calculate total population of Arains.
(29295000x1540%)=451143000.
The above mentioned figures are calculated on estimation of every 100 years for first 3 centuries, it could be increase if we calculate it on growth rate of 220% for every 100year.

Now every one can see the estimated population of Arains in the world that should be round about Forty Five Karors 45000000. This figure is much higher then the actual population of Arains which is about Six Karor 60,000,000. Why? This figure is an answer to them who believe that Arains were not a fighter cast. Than what is the reason of their lesser population than the normally estimated Arain population. The only reason that could be establish here is their fighting background and we can say that Arains have a history of fighters more than any other cast living here in subcontinent. Arains are the sons of fighters and worriers. They fought thousand wars and millions of them had died in those fights.