How many bacteria are produced in four hours if a bacterium divides once in half an hour ?

Options

A. 8
B. 64
C. 16
D. 256

Answer

To solve the problem of how many bacteria are produced in four hours if a bacterium divides once every half an hour, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the total time of division**:
- We know that the bacterium divides every half an hour. In four hours, we need to find out how many half-hour intervals there are.
- Total time = 4 hours = 4 * 60 minutes = 240 minutes.
- Each division takes 30 minutes, so the number of divisions (n) in 4 hours is:
\[ n = \frac{240 \text{ minutes}}{30 \text{ minutes/division}} = 8 \text{ divisions}. \]

2. **Use the formula for bacterial growth**:
- The total number of bacteria produced can be calculated using the formula:
\[ \text{Total number of bacteria} = 2^n, \]
where n is the number of divisions.

3. **Calculate the total number of bacteria**:
- Substitute n = 8 into the formula:
\[ \text{Total number of bacteria} = 2^8. \]
- Now calculate \(2^8\):
\[ 2^8 = 256. \]

4. **Conclusion**:
- Therefore, the total number of bacteria produced in four hours is **256**.

### Final Answer:
The correct answer is **256**.