Answer:
14 years
Step-by-step explanation:
You want to know the time it takes for a GDP of $15,000 per person to grow to $60,000 per person at the rate of 10% per year.
If the GDP doubles, it will be $30,000 after about 70/10 = 7 years.
If it doubles again, it will be $60,000 after 7 more years.
The GDP will be about $60,000 per person after 14 years.
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Additional comment
A more exact calculation gives the time as 14.5 years, so the approximation has an error of less than 4%.