A bacterium growing on an agar surface divides. Most bacteria are not very motile on solid surface. The progeny of bacteria remain very near to the location of original bacterium. If 10 cells are plated and a cell takes 30 minutes to multiply then number of colonies visible, next day would be

Options

A. 10
B. `10^(2)`
C. `10^(4)`
D. `10^(8)`

Explanation

To solve the problem of how many colonies will be visible the next day after plating 10 bacterial cells that each take 30 minutes to multiply, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- We start with 10 bacterial cells plated on an agar surface.
- Each bacterium takes 30 minutes to divide.

2. **Division Process**:
- In 30 minutes, each bacterium divides into 2 cells (1 original + 1 new).
- After the first 30 minutes, we will have:
- 10 original cells × 2 = 20 cells.

3. **Further Division**:
- After another 30 minutes (total 1 hour), each of the 20 cells will divide again.
- So, after 1 hour, we will have:
- 20 cells × 2 = 40 cells.

4. **Continuing the Process**:
- This process continues every 30 minutes.
- After 1.5 hours (90 minutes), we will have:
- 40 cells × 2 = 80 cells.
- After 2 hours (120 minutes), we will have:
- 80 cells × 2 = 160 cells.
- After 2.5 hours (150 minutes), we will have:
- 160 cells × 2 = 320 cells.
- After 3 hours (180 minutes), we will have:
- 320 cells × 2 = 640 cells.

5. **Calculating the Number of Colonies**:
- Since bacteria are not very motile and remain near their original location, each original bacterium will form a colony.
- Therefore, the number of colonies will be equal to the number of original cells plated, which is 10.

6. **Final Answer**:
- The number of colonies visible the next day will be **10**.