To find the number of bacteria after 512 hours, we can substitute \( h = 512 \) into the function \( B(h) = 82(1.25)^h \).
Calculating \( B(512) \):
\[ B(512) = 82(1.25)^{512} \]
To calculate \( (1.25)^{512} \), we can use a calculator:
\[ (1.25)^{512} \approx 3.203 \times 10^{9} \]
Now, multiply this value by 82:
\[ B(512) \approx 82 \times 3.203 \times 10^{9} \approx 2.628 \times 10^{11} \]
Thus, rounding to the nearest whole number, the number of bacteria after 512 hours is approximately \( 262800000000 \).
If we have to choose from the provided options, it appears that none of the options are remotely close to this number; let me know if you provide more choices or if you'd like to analyze this more.