To find the increase in the U.S. national debt from 1971 to 2021, we can subtract the debt in 1971 from the debt in 2021.
The national debt in 2021 is \( 2.9617 \times 10^{13} \) and in 1971 it is \( 3.98 \times 10^{11} \).
First, we need to express these numbers in a compatible format.
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National debt in 2021: \[ 2.9617 \times 10^{13} = 29,617,000,000,000 \]
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National debt in 1971: \[ 3.98 \times 10^{11} = 398,000,000,000 \]
Now we can subtract the two values:
\[ \text{Increase in debt} = \text{Debt in 2021} - \text{Debt in 1971} \] \[ = (2.9617 \times 10^{13}) - (3.98 \times 10^{11}) \]
Since \( 3.98 \times 10^{11} \) is much smaller than \( 2.9617 \times 10^{13} \), we can directly subtract the numbers:
\[ = 2.9617 \times 10^{13} - 0.398 \times 10^{13} \] \[ = (2.9617 - 0.398) \times 10^{13} \] \[ = 2.5637 \times 10^{13} \]
Thus, the increase in the national debt over the 50-year period from 1971 to 2021 is approximately \( 2.5637 \times 10^{13} \) dollars.
To give a more intuitive understanding: \[ 2.5637 \times 10^{13} = 25,637,000,000,000 \]
Therefore, the U.S. national debt increased by approximately $25.64 trillion over that 50-year period.