To find the number of bacteria after 5.5 hours using the function \( B(h) = 82(1.25)^h \), we will substitute \( h = 5.5 \) into the equation.
\[ B(5.5) = 82(1.25)^{5.5} \]
Now, we first calculate \( (1.25)^{5.5} \):
\[ (1.25)^{5.5} \approx 3.208 \]
Now we can calculate \( B(5.5) \):
\[ B(5.5) \approx 82 \times 3.208 \approx 263.056 \]
Rounding this to the nearest whole number gives us approximately 263.
Therefore, there are approximately 263 bacteria after 5.5 hours.
However, if we only consider provided options, 263 is not listed. Given the closest options:
- 280
- 278
- 257
- 564
The most appropriate estimate of the bacteria count based on the choices provided would be 257.