Bacteria is known to grow exponentially. The function B(h)=82(1.25)h

Question

represents the number of bacteria, B(h)
, as a function of hours, h. How many bacteria will there be after only 512
hours to the nearest bacteria? What is B(512)

Answer 1

To find the number of bacteria after 512 hours using the function \( B(h) = 82(1.25)^h \), we can substitute \( h = 512 \) into the formula:

\[ B(512) = 82(1.25)^{512} \]

Now, calculate \( (1.25)^{512} \) first:

Using a calculator, we find:

\[ (1.25)^{512} \approx 1.082866 \times 10^{16} \]

Now, multiply by 82:

\[ B(512) \approx 82 \times 1.082866 \times 10^{16} \approx 8.89508172 \times 10^{17} \]

To the nearest whole number, this would be:

\[ B(512) \approx 889508172000000000 \]

Thus, the number of bacteria after 512 hours is approximately 889,508,172,000,000,000.