A bacterium divides every 35 minutes. If a culture containing `10^(5)` cells/ml is grown for 2 hours 55 minutes, what will be the cell concentration per ml?

Options

A. `32 xx 10^(5)` cells
B. `35 xx 10^(5)` cells
C. `64 xx 10^(5)` cells
D. `5 xx 10^(5)` cells

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the division time
A bacterium divides every 35 minutes. This means that every 35 minutes, the number of bacteria doubles.

### Step 2: Convert the total growth time into minutes
The total time given is 2 hours and 55 minutes. We need to convert this into minutes:
- 2 hours = 2 × 60 = 120 minutes
- Total time = 120 minutes + 55 minutes = 175 minutes

### Step 3: Calculate the number of generations
To find out how many generations occur in 175 minutes, we divide the total time by the division time:
- Number of generations = Total time / Division time = 175 minutes / 35 minutes = 5 generations

### Step 4: Calculate the final concentration of bacteria
Initially, we have a concentration of \(10^5\) cells/ml. After each generation, the number of cells doubles. Therefore, after 5 generations, the number of cells will be:
- Final concentration = Initial concentration × \(2^{\text{number of generations}}\)
- Final concentration = \(10^5 \times 2^5\)

### Step 5: Calculate \(2^5\)
We know that \(2^5 = 32\).

### Step 6: Calculate the final concentration
Now we can substitute \(2^5\) into the equation:
- Final concentration = \(10^5 \times 32 = 32 \times 10^5\) cells/ml.

### Conclusion
The final cell concentration after 2 hours and 55 minutes will be \(32 \times 10^5\) cells/ml.

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