After 6 generations of mitosis from a single cell, half of the cells are found entering `G_(0)` phase and the remaining half undergo 3 more generations of mitotic divisions. The total number of cells of that system are

Options

A. 288
B. 64
C. 256
D. 192

Answer

To solve the problem, we will break it down step by step.

### Step 1: Calculate the number of cells after 6 generations of mitosis.
- Starting with 1 cell, each generation of mitosis doubles the number of cells.
- The formula for the number of cells after \( n \) generations of mitosis is \( 2^n \).
- After 6 generations:
\[ \text{Number of cells} = 2^6 = 64 \]

### Step 2: Determine how many cells enter the G0 phase.
- According to the problem, half of the cells enter the G0 phase.
- Therefore, the number of cells entering G0 is:
\[ \text{Cells in G0} = \frac{64}{2} = 32 \]

### Step 3: Calculate the remaining cells that undergo 3 more generations of mitotic divisions.
- The remaining cells after half enter G0 are also 32 (since 64 - 32 = 32).
- These 32 cells will undergo 3 more generations of mitosis.
- After each generation, the number of cells doubles:
- After the 1st generation:
\[ 32 \times 2 = 64 \]
- After the 2nd generation:
\[ 64 \times 2 = 128 \]
- After the 3rd generation:
\[ 128 \times 2 = 256 \]

### Step 4: Calculate the total number of cells in the system.
- Now, we add the cells in G0 phase and the cells after the 3 additional generations:
\[ \text{Total cells} = \text{Cells in G0} + \text{Cells after 3 generations} = 32 + 256 = 288 \]

### Final Answer:
The total number of cells in the system is **288**.

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