To find the increase in the national debt from 1971 to 2021, we subtract the national debt in 1971 from the national debt in 2021.
Given:
- National debt in 2021 = \( 2.9617 \times 10^{13} \)
- National debt in 1971 = \( 3.98 \times 10^{11} \)
We can perform the subtraction:
\[ \text{Increase in debt} = (2.9617 \times 10^{13}) - (3.98 \times 10^{11}) \]
To make the calculation easier, let's express \( 3.98 \times 10^{11} \) in terms of \( 10^{13} \):
\[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]
Now we can rewrite the equation:
\[ \text{Increase in debt} = (2.9617 \times 10^{13}) - (0.0398 \times 10^{13}) \]
This simplifies to:
\[ \text{Increase in debt} = (2.9617 - 0.0398) \times 10^{13} \]
Now, performing the subtraction:
\[ 2.9617 - 0.0398 = 2.9219 \]
Thus, we have:
\[ \text{Increase in debt} = 2.9219 \times 10^{13} \]
Therefore, the increase in the national debt over the 50-year period is:
\[ \boxed{2.9219 \times 10^{13}} \]