How many mitotic divisions are needed for a single cell to make 128cells

Options

A. 7
B. 14
C. 28
D. 64

Explanation

To determine how many mitotic divisions are needed for a single cell to produce 128 cells, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the process of mitosis**: Each time a cell undergoes mitosis, it divides into two daughter cells. Therefore, after one mitotic division, one cell becomes two cells.

2. **Identify the relationship**: If a single cell undergoes 'n' mitotic divisions, the total number of cells produced can be expressed as \(2^n\). This is because each division doubles the number of cells.

3. **Set up the equation**: We need to find 'n' such that the total number of cells equals 128. Thus, we set up the equation:
\[ 2^n = 128 \]

4. **Express 128 as a power of 2**: We can rewrite 128 in terms of powers of 2. We know that:
\[ 128 = 2^7 \]

5. **Compare the exponents**: Since we have \(2^n = 2^7\), we can equate the exponents:
\[ n = 7 \]

6. **Conclusion**: Therefore, the number of mitotic divisions needed for a single cell to make 128 cells is 7.

### Final Answer:
The correct answer is A - 7.

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