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)?

Answer 1

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

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

\[
(1.25)^{5.5} \approx 2.250618
\]

Now, we substitute this back into the equation for \( B(h) \):

\[
B(5.5) = 82 \times (1.25)^{5.5} \approx 82 \times 2.250618
\]

Now, performing the multiplication:

\[
B(5.5) \approx 185.80
\]

Rounding to the nearest bacteria:

\[
B(5.5) \approx 186
\]

Thus, after 5.5 hours, there will be approximately \( \boxed{186} \) bacteria.