A scientist studies Bacteria Culture A, which grows then percent every hour. Bacteria Culture A initially contained 200 microbes, and she models the growth using the equation `n=200(m)^(h)`, where n is the number of microbes and h is the number of hours.
Q. The same scientist also studies another culture, Bacteria Culture B, which grows 15% every hour. The two cultures began at the same time with the same number of microbes. After 20 hours, how many more microbes will becteria Culture B contain than Bacteria Culture A ? (Round your answer to the nearest whole number).

Answer

To solve the problem, we need to calculate the number of microbes in both Bacteria Culture A and Bacteria Culture B after 20 hours and then find the difference between the two.

### Step-by-Step Solution:

1. **Identify the growth equations for both cultures:**
- For Bacteria Culture A, which grows at 10% per hour:
\[ n_A = 200 \times (1 + 0.10)^h = 200 \times (1.1)^h \]
- For Bacteria Culture B, which grows at 15% per hour:
\[ n_B = 200 \times (1 + 0.15)^h = 200 \times (1.15)^h \]

2. **Substitute \( h = 20 \) into both equations:**
- For Bacteria Culture A:
\[ n_A = 200 \times (1.1)^{20} \]
- For Bacteria Culture B:
\[ n_B = 200 \times (1.15)^{20} \]

3. **Calculate \( (1.1)^{20} \) and \( (1.15)^{20} \):**
- Using a calculator:
\[ (1.1)^{20} \approx 6.7275 \]
\[ (1.15)^{20} \approx 16.3668 \]

4. **Calculate the number of microbes in each culture:**
- For Bacteria Culture A:
\[ n_A = 200 \times 6.7275 \approx 1345.5 \]
- For Bacteria Culture B:
\[ n_B = 200 \times 16.3668 \approx 3273.36 \]

5. **Find the difference between the two cultures:**
- The difference \( n_B - n_A \):
\[ n_B - n_A = 3273.36 - 1345.5 \approx 1927.86 \]

6. **Round the answer to the nearest whole number:**
- Rounding \( 1927.86 \) gives us \( 1928 \).

### Final Answer:
Bacteria Culture B contains **1928 more microbes** than Bacteria Culture A after 20 hours.

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