# 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 =  4.82081413278E+60

#### Solution:

$n_{ 0 } = 2 \ \\ n_{ 35 } = n_{ 0 }+1 \cdot \ 4 = 2+1 \cdot \ 4 = 6 \ \\ n_{ 75 } = n_{ 35 } - 2 + 2 \cdot \ 4 = 6 - 2 + 2 \cdot \ 4 = 12 \ \\ n_{ 100 } = n_{ 75 } - 4 + 4 \cdot \ 4 = 12 - 4 + 4 \cdot \ 4 = 24 \ \\ \ \\ a_{ 1 } = n_{ 35 } = 6 \ \\ a_{ 2 } = n_{ 75 } = 12 \ \\ a_{ 3 } = n_{ 100 } = 24 \ \\ q = a_{ 2 }/a_{ 1 } = 12/6 = 2 \ \\ q = a_{ 3 }/a_{ 2 } \ \\ \ \\ n = 5000 / 25 - 1 = 199 \ \\ \ \\ s = a_{ 1 } \cdot \ q^{ n } = 6 \cdot \ 2^{ 199 } = 4.82081413278\cdot 10^\{ 60 \} = 4.82081413278\cdot 10^{ 60 }$

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