Bacteria is known to grow exponentially. The function represents the
number of bacteria, , as a function of hours, . How many bacteria will there be after only
hours to the nearest bacteria? What is ? (1 point)
279
564
280
257

Ask by Macdonald George. in the United States

Mar 24,2025

Question

Bacteria is known to grow exponentially. The function represents the
number of bacteria, , as a function of hours, . How many bacteria will there be after only
hours to the nearest bacteria? What is ? (1 point)
279
564
280
257

Ask by Macdonald George. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

We are given the function

$$
B(h) = 82(1.25)^h
$$

and we need to find

$$
B\left(5\frac{1}{2}\right) = B(5.5).
$$

Step 1. Substitute $$ h = 5.5 $$ into the function:

$$
B(5.5) = 82(1.25)^{5.5}.
$$

Step 2. Rewrite $$ (1.25)^{5.5} $$ using the exponential function:

$$
(1.25)^{5.5} = e^{5.5 \ln(1.25)}.
$$

Step 3. Compute $$ 5.5 \ln(1.25) $$.

Using an approximation, note that

$$
\ln(1.25) \approx 0.223144,
$$

so

$$
5.5 \ln(1.25) \approx 5.5 \times 0.223144 \approx 1.227292.
$$

Step 4. Compute the exponential:

$$
e^{1.227292} \approx 3.412.
$$

Step 5. Multiply by 82:

$$
B(5.5) \approx 82 \times 3.412 \approx 279.784.
$$

Step 6. Round to the nearest whole number, resulting in

$$
B(5.5) \approx 280.
$$

Thus, after $$5\frac{1}{2}$$ hours there will be $$\boxed{280}$$ bacteria.
After $$5\frac{1}{2}$$ hours, there will be approximately 280 bacteria.