A bacterium divides in every 20 minutes. How many bacteria will be formed within three hours?

Options

A. 18
B. 36
C. 256
D. 512

Answer

To solve the problem of how many bacteria will be formed within three hours when a bacterium divides every 20 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the total time in minutes for three hours**:
- There are 60 minutes in an hour. Therefore, in three hours:
\[ 3 \text{ hours} \times 60 \text{ minutes/hour} = 180 \text{ minutes} \]

2. **Calculate the number of division cycles (trials) that occur in 180 minutes**:
- Since the bacterium divides every 20 minutes, we can find the number of divisions by dividing the total time by the time per division:
\[ \text{Number of trials} = \frac{180 \text{ minutes}}{20 \text{ minutes/trial}} = 9 \text{ trials} \]

3. **Use the formula for exponential growth of bacteria**:
- Each division results in the doubling of the bacteria. Therefore, if we start with one bacterium, the total number of bacteria after \( n \) divisions is given by:
\[ \text{Total bacteria} = 2^n \]
- In this case, \( n = 9 \):
\[ \text{Total bacteria} = 2^9 = 512 \]

4. **Conclusion**:
- Therefore, the total number of bacteria formed within three hours is **512**.

### Final Answer:
The number of bacteria formed within three hours is **512**.

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