A cell's division time is 1 minute. In 20 minutes, a culture tube (culture medium) is `1//8^(th)` filled with cells. When the tube will be fully filled?

Options

A. (a) 21 minutes
B. (b) 23 minutes
C. (c) 60 minutes
D. (d) 160 minutes

Explanation

To solve the problem, we need to determine how long it will take for the culture tube to be fully filled with cells, given that the division time of a cell is 1 minute and that after 20 minutes, the tube is 1/8 filled with cells.

### Step-by-Step Solution:

1. **Understand the Division Process**:
- Each cell divides into two cells every minute. This means that the number of cells doubles every minute.

2. **Calculate the Number of Cells After 20 Minutes**:
- After 20 minutes, the culture tube is 1/8 filled. This means that at 20 minutes, if we denote the number of cells at that time as \( N \), then:
\[ N = \text{(initial number of cells)} \times 2^{20} \]
- Since the tube is 1/8 filled, we can infer that the number of cells at 20 minutes is \( N = \frac{1}{8} \).

3. **Determine the Filling Rate**:
- Since the cells double every minute, we can find out how much the tube will be filled in the next minutes:
- At 21 minutes, the tube will be \( \frac{1}{8} \times 2 = \frac{1}{4} \) filled.
- At 22 minutes, the tube will be \( \frac{1}{4} \times 2 = \frac{1}{2} \) filled.
- At 23 minutes, the tube will be \( \frac{1}{2} \times 2 = 1 \) (fully filled).

4. **Conclusion**:
- Therefore, the culture tube will be fully filled with cells in 23 minutes.

### Final Statement:
Hence, the culture tube will be fully filled with cells in **23 minutes**.