In a culture of E.coli the cell population increased from `1.5 xx 10^(6)` cells/ml to `12 xx 10^(6)` cells/ml in 36 minutes. The generation time is

Options

A. 6 min.
B. 9 min.
C. 12 min.
D. 18 min.

Explanation

To find the generation time for the E. coli culture, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial and Final Cell Counts**:
- Initial cell count (N0) = \(1.5 \times 10^6\) cells/ml
- Final cell count (N) = \(12 \times 10^6\) cells/ml

2. **Calculate the Increase in Cell Count**:
- To find out how many times the population has increased, we can divide the final count by the initial count:
\[ \text{Increase Factor} = \frac{N}{N0} = \frac{12 \times 10^6}{1.5 \times 10^6} = 8 \]

3. **Determine the Number of Generations**:
- The increase factor of 8 means the population has increased 8 times. To find out how many generations (or divisions) this corresponds to, we can use the formula:
\[ \text{Increase Factor} = 2^n \]
where \(n\) is the number of generations. We need to solve for \(n\):
\[ 2^n = 8 \implies n = 3 \quad (\text{since } 2^3 = 8) \]

4. **Calculate the Total Time for Divisions**:
- We know that these 3 divisions occurred over a total time of 36 minutes.

5. **Calculate the Generation Time**:
- The generation time (time per division) can be calculated by dividing the total time by the number of divisions:
\[ \text{Generation Time} = \frac{\text{Total Time}}{n} = \frac{36 \text{ minutes}}{3} = 12 \text{ minutes} \]

### Final Answer:
The generation time for E. coli in this culture is **12 minutes**.

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