To model the number of words \( y \) that the AI learns after \( x \) hours, we start with the fact that the AI knows 125 words initially and doubles its vocabulary every 8 hours.
- Initially, the number of words \( y_0 = 125 \).
- After 8 hours, \( y = 125 \times 2^1 \).
- After 16 hours, \( y = 125 \times 2^2 \).
- After \( x \) hours, where \( n \) is the number of 8-hour periods in \( x \) hours, we can represent it as \( y = 125 \times 2^{(x/8)} \).
Now we can identify that we can write \( 125 \) as \( 2^7 \cdot 1.25 \) for conversion in exponential form or continue with our formula:
The equation can be represented as:
\[ y = 125 \times 2^{(x/8)} \]
Since the doubling occurs every 8 hours, we can rewrite \( 2^{(x/8)} \) in terms of base \( 2 \).
However, none of the provided choices state the equation exactly in the correct manner or format.
If we analyze the durations:
- The doubling relationships are not reflected in terms of constants in the options for \( 8 \) or \( 2.5 \).
Therefore, none of the options correctly model the equation for words learned after \( x \) hours.
In conclusion, the answer to the question as provided does not reflect in one of the options based on the understanding of the exponential growth of vocabulary based on the provided time ratio.
If following closely with the closest reinterpretation we refuse the options, however \( y = 125 \times 2^{(x/8)} \) should have been provided or calculated into acceptable options.