The number of mitotic division that must occur in a cell of the root tip to form 256 cells is

Options

A. 256
B. 128
C. 7
D. 8

Answer

To determine the number of mitotic divisions required to form 256 cells from a single cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mitosis**: Each mitotic division of a single cell results in the formation of two cells. Therefore, if we start with one cell, the number of cells after each division can be represented as powers of 2.

2. **Setting Up the Equation**:
- After 0 divisions (starting point): \(2^0 = 1\) cell
- After 1 division: \(2^1 = 2\) cells
- After 2 divisions: \(2^2 = 4\) cells
- After 3 divisions: \(2^3 = 8\) cells
- After 4 divisions: \(2^4 = 16\) cells
- After 5 divisions: \(2^5 = 32\) cells
- After 6 divisions: \(2^6 = 64\) cells
- After 7 divisions: \(2^7 = 128\) cells
- After 8 divisions: \(2^8 = 256\) cells

3. **Counting the Divisions**: To find how many divisions are needed to reach 256 cells, we can see from our calculations that:
- \(2^8 = 256\)

4. **Conclusion**: Therefore, the number of mitotic divisions that must occur to form 256 cells is **8**.

### Final Answer:
The number of mitotic divisions required to form 256 cells is **8**.

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