cell undergoes mitosis in 30 minutes. Find the number of cells produced after 24 hours if initially `10^(5)` cells are present.

Options

A. `2^(24) xx 10^(5)`
B. `2^(48) xx 10^(5)`
C. `2^(48) + 10^(5)`
D. `48 xx 10^(5-)`

Answer

To solve the problem of how many cells are produced after 24 hours when a cell undergoes mitosis every 30 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the number of cell cycles in 24 hours**:
- Since one cell undergoes mitosis every 30 minutes, we need to find out how many 30-minute intervals are in 24 hours.
- There are 60 minutes in an hour, so in 24 hours, there are:
\[ 24 \text{ hours} \times 60 \text{ minutes/hour} = 1440 \text{ minutes} \]
- Now, divide the total minutes by the duration of one cell cycle (30 minutes):
\[ \frac{1440 \text{ minutes}}{30 \text{ minutes/cycle}} = 48 \text{ cycles} \]

2. **Calculate the number of cells after 48 cycles**:
- Each cell division results in doubling the number of cells. Therefore, after \( n \) cycles, the number of cells can be expressed as:
\[ 2^n \]
- For 48 cycles, the number of cells produced from one initial cell is:
\[ 2^{48} \]

3. **Consider the initial number of cells**:
- The problem states that we start with \( 10^5 \) cells. Thus, the total number of cells after 48 cycles will be:
\[ \text{Total cells} = \text{Initial cells} \times \text{Cells produced from one cell} \]
- This gives us:
\[ \text{Total cells} = 10^5 \times 2^{48} \]

4. **Final expression**:
- Therefore, the final answer for the number of cells produced after 24 hours is:
\[ 10^5 \times 2^{48} \]