Hello!
GDP per person is total GDP divided by a population size. Let's denote the initial GDP as and the initial population size as
Then the initial GDP per person is
After a year, GDP will grow by 12 percent and becomes A population will grow by 10 percent and becomes
So GDP per person becomes
After each next year GDP per person will be multiplied by the...
Hello!
GDP per person is total GDP divided by a population size. Let's denote the initial GDP as and the initial population size as
Then the initial GDP per person is
After a year, GDP will grow by 12 percent and becomes A population will grow by 10 percent and becomes
So GDP per person becomes
After each next year GDP per person will be multiplied by the same factor, Thus after
years it becomes
And the problem is to find such that
or
To solve this equation it is necessary to use logarithms. Take natural logarithm on both sides:
This is equal to approximately 38.5. Therefore it will take 39 full years for real GDP per person to double.
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