Hello!

GDP per person is total GDP divided by a population size. Let's denote the initial GDP as `A` and the initial population size as `B.` Then the initial GDP per person is `A/B.`

After a year, GDP will grow by 12 percent and becomes `A*1.12.` A population will...

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Hello!

GDP per person is total GDP divided by a population size. Let's denote the initial GDP as `A` and the initial population size as `B.` Then the initial GDP per person is `A/B.`

After a year, GDP will grow by 12 percent and becomes `A*1.12.` A population will grow by 10 percent and becomes `B*1.10.` So GDP per person becomes `A/B*1.12/1.1.`

After each next year GDP per person will be multiplied by the same factor, `1.12/1.1.` Thus after `n` years it becomes `A/B*(1.12/1.1)^n.`

And the problem is to find such `n` that `A/B*(1.12/1.1)^n=A/B*2,` or `(1.12/1.1)^n=2.`

To solve this equation it is necessary to use logarithms. Take natural logarithm on both sides:

`n*ln(1.12/1.1)=ln(2), or n=ln(2)/(ln(1.12/1.1)).`

This is equal to approximately 38.5. Therefore it will take **39** full years for real GDP per person to double.