Final answer:
By applying the rule of 70 to the GDP per capita growth rate of 8% (10% GDP growth minus 2% population growth), we find that it will take approximately 8.75 years for China's GDP per capita to double from its 2014 value. Rounding up to 9 years, China's GDP per capita will double by 2023.
Step-by-step explanation:
When considering that in 2014 China's real GDP is growing at 10 percent per year and its population is growing at 2.0 percent per year, we need to calculate the growth rate of GDP per capita. The growth rate of GDP per capita is essentially the growth rate of the total GDP minus the growth rate of the population, which in this case is 10% - 2% = 8% per year.
Now, to determine when China's real GDP per person will be double its 2014 value, we use the rule of 70, which is a quick way to estimate the number of years required to double at a constant annual growth rate. According to this rule, you divide 70 by the annual growth rate to find the doubling time in years. Therefore, we divide 70 by the GDP per capita growth rate, which is 70 / 8 = 8.75 years. Since the base year is 2014, adding approximately 9 years (as we only have full year options) gives us 2014 + 9 = 2023.