How many equational divisions are necessary in a cell of onion root tip to form 128 cells?

Options

A. 64
B. 128
C. 7
D. None of these

Answer

To determine how many equational divisions (mitotic divisions) are necessary to form 128 cells from a single cell in the onion root tip, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mitosis**: Mitosis is the type of cell division that results in two daughter cells that are genetically identical to the parent cell. Each division doubles the number of cells.

2. **Starting Point**: We start with 1 cell.

3. **Cell Doubling**: Each mitotic division results in the doubling of the number of cells.
- After 1 division: 2 cells
- After 2 divisions: 4 cells
- After 3 divisions: 8 cells
- After 4 divisions: 16 cells
- After 5 divisions: 32 cells
- After 6 divisions: 64 cells
- After 7 divisions: 128 cells

4. **Calculating Divisions**: To find out how many divisions are needed to reach 128 cells, we can use the formula:
\[ \text{Number of cells} = 2^n \]
where \( n \) is the number of divisions. We need to find \( n \) such that:
\[ 2^n = 128 \]

5. **Solving for n**: We know that:
\[ 128 = 2^7 \]
Therefore, \( n = 7 \).

6. **Conclusion**: To form 128 cells, 7 equational divisions (mitotic divisions) are necessary.

### Final Answer:
7 equational divisions are necessary to form 128 cells.