If the generation time of a bacterium is 35 minutes. What will be the cell concentration per ml in a culture containing 10 cells per ml grown for 175 minutes ?

Options

A. `32 xx10^(5)` cells
B. `45 xx 10^(8)` cells
C. `5xx10^(5)` cells
D. `0.32 x 10^(5)` cells

Answer

To solve the problem of determining the cell concentration per ml in a culture containing 10 cells per ml grown for 175 minutes, given a generation time of 35 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Generation Time**: The generation time of 35 minutes means that every 35 minutes, the number of bacteria doubles.

2. **Calculate the Number of Generations**: To find out how many generations occur in 175 minutes, we divide the total time by the generation time:
\[ \text{Number of Generations} = \frac{175 \text{ minutes}}{35 \text{ minutes/generation}} = 5 \text{ generations} \]

3. **Initial Cell Concentration**: The initial concentration of the culture is given as 10 cells per ml.

4. **Calculate the Final Cell Concentration**: After each generation, the number of cells doubles. Therefore, after \( n \) generations, the final concentration can be calculated using the formula:
\[ \text{Final Concentration} = \text{Initial Concentration} \times 2^{\text{Number of Generations}} \]
Substituting the values:
\[ \text{Final Concentration} = 10 \text{ cells/ml} \times 2^5 \]

5. **Calculate \( 2^5 \)**:
\[ 2^5 = 32 \]

6. **Final Calculation**: Now, substituting back into the equation:
\[ \text{Final Concentration} = 10 \text{ cells/ml} \times 32 = 320 \text{ cells/ml} \]

### Final Answer:
The cell concentration per ml in the culture after 175 minutes will be **320 cells/ml**.

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