A bacterium divides every `35` minutes. If a culture containing `10^(5)` cells/ml is grown for `175` minutes. What will be the cell concentration / ml after `175` minutes

Options

A. `32 xx 10^(5)` cells
B. `5 xx 10^(5)` cells
C. `35 xx 10^(5)` cells
D. `175 xx 10^(5)` cells

Explanation

To solve the problem of how many cells per ml will be present after 175 minutes of growth for a bacterium that divides every 35 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Initial Cell Count**:
The initial concentration of the bacterial culture is given as \(10^5\) cells/ml.

2. **Calculate the Total Time of Growth**:
The total time for which the bacteria are allowed to grow is 175 minutes.

3. **Determine the Time for Each Division**:
Each bacterium divides every 35 minutes.

4. **Calculate the Number of Divisions**:
To find out how many times the bacteria divide in 175 minutes, we divide the total time by the time for each division:
\[ \text{Number of divisions} = \frac{175 \text{ minutes}}{35 \text{ minutes/division}} = 5 \text{ divisions} \]

5. **Calculate the Final Cell Count**:
Since the bacteria double in number with each division, we can express the final cell count after 5 divisions as:
\[ \text{Final cell count} = \text{Initial count} \times 2^{\text{Number of divisions}} = 10^5 \times 2^5 \]
We know \(2^5 = 32\), so:
\[ \text{Final cell count} = 10^5 \times 32 = 32 \times 10^5 \text{ cells/ml} \]

6. **Conclusion**:
After 175 minutes, the concentration of cells will be \(32 \times 10^5\) cells/ml.

### Final Answer:
The final concentration of cells after 175 minutes is **32 x \(10^5\) cells/ml**.

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