False.
RGDP Per Capita = RGDP/population
If the population grows faster than real GDP, that means the denominator grows large more quickly than the numerators. So the fraction is growing smaller.
Another way you could think about this intuitively is to think of real GDP as the amount of food a family has available to eat. If the family grows more quickly than the total amount of food, then each person will have less to eat.
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