Question

Over the past 100 years, U.S. real GDP per person has doubled about every 35 years. If, in the next 100 years, it doubles every 25 years, then a century from now U.S. real GDP per person will be ______ times higher than it is now.

1) 2 times higher than it is now
2) 4 times higher than it is now
3) 8 times higher than it is now
4) 16 times higher than it is now

Answer 1

The U.S. real GDP per person will be 2 times higher than it is now in a century.

Step-by-step explanation:

To determine how many times higher the U.S. real GDP per person will be in a century if it doubles every 25 years, we need to find the number of times it doubles. Since it currently doubles every 35 years, we can calculate the ratio of the new doubling period to the old doubling period: 35/25 = 7/5. This means the U.S. real GDP per person will double 7/5 times in a century. Mathematically, this is represented as 2^(7/5). Approximating this value, we find that 2^(7/5) ≈ 2.00. Therefore, a century from now, the U.S. real GDP per person will be 2 times higher than it is now.