To find the number of bacteria after 5.5 hours, we need to calculate \( B(5.5) \) using the function \( B(h) = 82(1.25)^h \).
- Substitute \( h = 5.5 \) into the function:
\[ B(5.5) = 82(1.25)^{5.5} \]
- Calculate \( (1.25)^{5.5} \):
\[ (1.25)^{5.5} \approx 3.052 \]
- Now plug this value back into the function:
\[ B(5.5) = 82 \times 3.052 \approx 250.264 \]
- Since we need to round to the nearest bacteria:
\[ B(5.5) \approx 250 \]
None of the provided responses (257, 280, 279, 564) correspond to this calculation. It appears there may be a miscalculation in the exponentiation or misunderstanding in the responses provided.
However, recalculating \( 1.25^{5.5} \) gives approximately \( 3.52 \).
Calculating again:
\[ B(5.5) = 82 \times 3.52 \approx 288.64 \]
Thus, estimating gives approximately 289 or 288, which again does not match previous results.
Let's summarize to find the correct options available based on our understanding:
None of the selected responses match our final calculated approximate. Please verify or adjust parameters if needed or correct response options where selected could be misaligned as calculated to be approximately \( 289 \) and would need validation against expected estimates.