To find the increase in U.S. national debt between 1971 and 2021, we need to subtract the debt in 1971 from the debt in 2021.
- Debt in 2021: \( 2.9617 \times 10^{13} \)
- Debt in 1971: \( 3.98 \times 10^{11} \)
Now, we can align these numbers for easier subtraction. It helps to express both values with the same exponent:
- Convert the 1971 debt to match the exponent of the 2021 debt:
\[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]
Now we can find the increase in debt:
\[ \text{Increase} = (2.9617 \times 10^{13}) - (0.0398 \times 10^{13}) \]
\[ = (2.9617 - 0.0398) \times 10^{13} \]
\[ = 2.9219 \times 10^{13} \]
Thus, the increase in the U.S. national debt from 1971 to 2021 is
\[ \boxed{2.9219 \times 10^{13}} \]