Answer: C. $y=34.4$

Explanation:1. Understand the scenario: In $8$ days, a polar bear ate a total of $34.4$ pounds of fat. The variable $y$ represents "the amount of fat y, in pounds, the polar bear ate in these 8 days".

2. Identify the direct information given: The problem explicitly states that the total amount of fat the polar bear ate in those $8$ days is $34.4$ pounds.

3. Relate this to the variable $y$: Since $y$ is defined as the amount of fat the polar bear ate in these $8$ days, and this amount is given as $34.4$ pounds, then $y = 34.4$.

4. Examine the options: [A] $y=8$ (This suggests the amount of fat is equal to the number of days, which is incorrect). [B] $y=\dfrac{34.4}{8}$ (This would represent the average amount of fat eaten per day, not the total amount eaten in $8$ days). [C] $y=34.4$ (This states that the amount of fat eaten in $8$ days is $34.4$ pounds, which matches the problem statement). [D] $y=34.4+8$ (This suggests adding the amount of fat to the number of days, which is contextually incorrect).

5. Conclusion: The equation that describes the amount of fat $y$, in pounds, the polar bear ate in these $8$ days is $y=34.4$. The question is essentially asking to identify the definition of $y$ based on the scenario.