To find how much the US national debt increased from 1971 to 2021, you need to subtract the debt in 1971 from the debt in 2021.
The values given are:
- National debt in 2021: \( 2.9617 \times 10^{13} \)
- National debt in 1971: \( 3.98 \times 10^{11} \)
Now let's perform the subtraction.
First, express both numbers in the same exponent form for easier calculation. You can express \( 3.98 \times 10^{11} \) with an exponent of \( 10^{13} \):
\[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]
Now you can perform the subtraction:
\[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} = 2.9219 \times 10^{13} \]
So, the increase in the national debt over the 50-year period is \( 2.9219 \times 10^{13} \).
Therefore, the correct answer is \( 2.9219 \times 10^{13} \).