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 1/2hours to the nearest bacteria? What is B(5 1/2)(1 point)

Answer 1

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

So we calculate:

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

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

\[ (1.25)^{5.5} \approx 2.953 \]

Now, substitute this value back into the equation:

\[ B(5.5) \approx 82 \times 2.953 \approx 242.086 \]

Rounding to the nearest bacteria gives us:

\[ B(5.5) \approx 242 \]

Thus, the estimated number of bacteria after 5.5 hours is 242.

Answer 2

wrong

Answer 3

Let’s recalculate \( B(5.5) \) using the function \( B(h) = 82(1.25)^h \).

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

   \[ (1.25)^{5.5} \approx 2.44140625 \]

2. Now, plug that value into the function:

   \[ B(5.5) = 82 \times (1.25)^{5.5} \approx 82 \times 2.44140625 \]

3. Now, perform the multiplication:

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

4. Rounding to the nearest whole number, we get:

   \[ B(5.5) \approx 200 \]

Thus, the corrected estimation for the number of bacteria after 5.5 hours is 200. Thank you for your patience!