Starting with a bacterium that divides once in half hour how many bacteria are formed after 24 hours of growth ?

Options

A. `2^(12)`
B. `2^(24)`
C. `2^(48)`
D. `2^(47)`

Answer

To solve the problem of how many bacteria are formed after 24 hours of growth, starting with a single bacterium that divides once every half hour, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Division Rate**: The bacterium divides once every half hour. This means that in one hour, it will divide twice.

2. **Calculate Divisions in One Hour**: Since the bacterium divides twice in one hour, we can say:
- Divisions in 1 hour = 2

3. **Calculate Total Hours in 24 Hours**: We need to find out how many times the bacterium will divide in 24 hours.
- Total hours = 24

4. **Calculate Total Divisions in 24 Hours**: Since the bacterium divides twice every hour:
- Total divisions in 24 hours = 2 divisions/hour × 24 hours = 48 divisions

5. **Use the Formula for Bacterial Growth**: The number of bacteria after n divisions can be calculated using the formula:
- Number of bacteria = \(2^n\)
- Here, \(n\) is the total number of divisions, which we calculated to be 48.

6. **Calculate the Total Number of Bacteria**:
- Number of bacteria after 24 hours = \(2^{48}\)

### Final Answer:
The total number of bacteria formed after 24 hours of growth is \(2^{48}\).

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