Bacteria is known to grow exponentially. The function B(h)=82(1.25)^h represents the number of bacteria, 𝐵(ℎ), as a function of hours, h. How many bacteria will there be after only 5 1/2 hours to the nearest bacteria?

Answer 1

To find the number of bacteria after 5.5 hours using the function \( B(h) = 82(1.25)^h \), we need to substitute \( h = 5.5 \) into the function.

Let's calculate:

\[ B(5.5) = 82(1.25)^{5.5} \]

First, we calculate \( (1.25)^{5.5} \):

\[ (1.25)^{5.5} \approx 2.44140625 \quad \text{(using a calculator)} \]

Now we substitute this back into the equation:

\[ B(5.5) = 82 \times 2.44140625 \approx 200.0 \]

Rounding to the nearest whole number, we find:

\[ B(5.5) \approx 200 \]

Therefore, the number of bacteria after 5.5 hours is approximately 200 bacteria.