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:

$$\begin{gathered} n_0=2 \\ {n}_{35}=n_0+1\cdot 4=2+1\cdot 4=6 \\ {n}_{75}=n_{35}-2+2\cdot 4=6-2+2\cdot 4=12 \\ {n}_{100}=n_{75}-4+4\cdot 4=12-4+4\cdot 4=24 \\ {a}_1=n_{35}=6 \\ {a}_2=n_{75}=12 \\ {a}_3=n_{100}=24 \\ q=a_2\mathrm{/}{a}_1=12\mathrm{/}6=2 \\ q=a_3\mathrm{/}{a}_2 \\ n=5000\mathrm{/}25-1=199 \\ s=a_1\cdot q^n=6\cdot 2^{199}=4.820814132777\cdot 10^{60} \end{gathered}$$

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