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?

Result

s =  4.820814132777E+60

Solution:

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

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