In a certain colony of cancerous cells , each cell divides into two every minute. How many cells will be produced from a single cell if the rate of division continues for 12 minutes :

Options

A. 9180
B. 8190
C. 8910
D. none of these

Answer

To solve the problem of how many cancerous cells will be produced from a single cell after 12 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Division Process**:
- Each cancerous cell divides into 2 cells every minute. This means that the number of cells doubles every minute.

2. **Identify the Pattern**:
- If we start with 1 cell, after:
- 1 minute: \( 1 \times 2 = 2 \) cells
- 2 minutes: \( 2 \times 2 = 4 \) cells
- 3 minutes: \( 4 \times 2 = 8 \) cells
- 4 minutes: \( 8 \times 2 = 16 \) cells
- 5 minutes: \( 16 \times 2 = 32 \) cells
- 6 minutes: \( 32 \times 2 = 64 \) cells
- 7 minutes: \( 64 \times 2 = 128 \) cells
- 8 minutes: \( 128 \times 2 = 256 \) cells
- 9 minutes: \( 256 \times 2 = 512 \) cells
- 10 minutes: \( 512 \times 2 = 1024 \) cells
- 11 minutes: \( 1024 \times 2 = 2048 \) cells
- 12 minutes: \( 2048 \times 2 = 4096 \) cells

3. **General Formula**:
- The number of cells after \( n \) minutes can be expressed as:
\[ \text{Number of cells} = 2^n \]
- For \( n = 12 \):
\[ \text{Number of cells} = 2^{12} = 4096 \]

4. **Conclusion**:
- After 12 minutes, starting from a single cell, there will be a total of **4096 cells**.

### Final Answer:
The total number of cells produced after 12 minutes is **4096**.

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