Population growth

How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?

Correct result:

s =  4.820814132777E+60

Solution:

$n_{0}=2 \ \\ n_{35}=n_{0}+1 \cdot \ 4=2+1 \cdot \ 4=6 \ \\ n_{75}=n_{35} - 2 + 2 \cdot \ 4=6 - 2 + 2 \cdot \ 4=12 \ \\ n_{100}=n_{75} - 4 + 4 \cdot \ 4=12 - 4 + 4 \cdot \ 4=24 \ \\ \ \\ a_{1}=n_{35}=6 \ \\ a_{2}=n_{75}=12 \ \\ a_{3}=n_{100}=24 \ \\ q=a_{2}/a_{1}=12/6=2 \ \\ q=a_{3}/a_{2} \ \\ \ \\ n=5000 / 25 - 1=199 \ \\ \ \\ s=a_{1} \cdot \ q^{ n }=6 \cdot \ 2^{ 199 }=4.820814132777\cdot 10^{ 60 }$

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