Question

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? What is B (5 1/2)?
564
280
279
257

Answer 1

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

Calculating \( B(5.5) \):

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

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

\[
(1.25)^{5.5} \approx 3.1748 \quad (\text{using a calculator})
\]

Now substitute this value back into the equation:

\[
B(5.5) = 82 \times 3.1748 \approx 260.14
\]

Now, we round \( 260.14 \) to the nearest whole number:

\[
B(5.5) \approx 260
\]

Now, check the provided options: 564, 280, 279, 257.

The nearest number from our calculation of approximately 260 is **257**.

Thus, the number of bacteria after 5.5 hours is:

\[
\boxed{257}
\]