When 16 cells are formed from a single cell, how many times cells divide and how many cells are formed in the 3rd generation?

Options

A. 4 and 8
B. 4 and 7
C. 3 and 8
D. 4 and 16

Answer

To solve the problem, we need to understand how many times a single cell divides to form 16 cells and how many cells are formed in the third generation.

### Step-by-Step Solution:

1. **Understanding Cell Division**:
- In mitosis, one parent cell divides to form two daughter cells. This means that each time a cell divides, the number of cells doubles.

2. **Calculating the Number of Divisions**:
- Let's denote the number of divisions as \( n \).
- After \( n \) divisions, the total number of cells formed can be calculated using the formula:
\[ \text{Total Cells} = 2^n \]
- We know that when 16 cells are formed, we can set up the equation:
\[ 2^n = 16 \]
- Since \( 16 = 2^4 \), we can conclude that:
\[ n = 4 \]
- Therefore, the cell divides 4 times to form 16 cells.

3. **Finding the Number of Cells in the Third Generation**:
- The first generation starts with 1 cell (the original parent cell).
- After the first division (1st generation), there are \( 2^1 = 2 \) cells.
- After the second division (2nd generation), there are \( 2^2 = 4 \) cells.
- After the third division (3rd generation), there are \( 2^3 = 8 \) cells.
- Thus, in the third generation, there are 8 cells.

### Final Answer:
- The number of times cells divide is **4**.
- The number of cells formed in the 3rd generation is **8**.