If a tissue has at a given time 1024 cells, how many cycles of mitosis had the original parental single cell undergone?

Options

A. 512
B. 10
C. 1024
D. 256

Explanation

To determine how many cycles of mitosis the original parental single cell underwent to produce 1,024 cells, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mitosis**:
- Mitosis is a process where one parent cell divides to form two daughter cells. Each daughter cell can then undergo mitosis, leading to exponential growth in the number of cells.

2. **Exponential Growth**:
- After each cycle of mitosis, the number of cells doubles. Therefore, if we denote the number of cycles of mitosis as \( n \), the number of cells after \( n \) cycles can be expressed as \( 2^n \).

3. **Setting Up the Equation**:
- We know that the total number of cells is 1,024. Thus, we can set up the equation:
\[ 2^n = 1024 \]

4. **Finding the Value of \( n \)**:
- To find \( n \), we need to express 1,024 as a power of 2.
- We can calculate the powers of 2:
- \( 2^1 = 2 \)
- \( 2^2 = 4 \)
- \( 2^3 = 8 \)
- \( 2^4 = 16 \)
- \( 2^5 = 32 \)
- \( 2^6 = 64 \)
- \( 2^7 = 128 \)
- \( 2^8 = 256 \)
- \( 2^9 = 512 \)
- \( 2^{10} = 1024 \)

5. **Conclusion**:
- From the calculations, we find that \( 1024 = 2^{10} \). Therefore, \( n = 10 \).
- This means the original parental cell underwent **10 cycles of mitosis** to produce 1,024 cells.

### Final Answer:
The original parental single cell underwent **10 cycles of mitosis**.