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. `32xx 10^5` cells
B. `5xx10^5` cells
C. `35xx10^5` cells
D. `4.175xx10^5`

Explanation

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Given Information
- The bacterium divides every 35 minutes.
- The initial concentration of the culture is \(10^5\) cells/ml.
- The total time for growth is 175 minutes.

### Step 2: Calculate the Number of Generations (n)
To find the number of generations (n), we use the formula:
\[ n = \frac{\text{Total Time}}{\text{Time per Division}} \]
Substituting the values:
\[ n = \frac{175 \text{ minutes}}{35 \text{ minutes}} = 5 \]

### Step 3: Use the Formula for Final Concentration
The formula for the final concentration of bacteria is:
\[ \text{Final Concentration} = \text{Initial Concentration} \times 2^n \]
Substituting the initial concentration and the number of generations:
\[ \text{Final Concentration} = 10^5 \times 2^5 \]

### Step 4: Calculate \(2^5\)
Calculating \(2^5\):
\[ 2^5 = 32 \]

### Step 5: Calculate the Final Concentration
Now substituting back into the formula:
\[ \text{Final Concentration} = 10^5 \times 32 = 32 \times 10^5 \text{ cells/ml} \]

### Step 6: Conclusion
The final concentration of the bacterial culture after 175 minutes is:
\[ \text{Final Concentration} = 32 \times 10^5 \text{ cells/ml} \]

### Final Answer
The correct answer is \(32 \times 10^5\) cells/ml.

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