Question

If a bacterial culture with a doubling time of 30 minutes starts with two cells, then the number of cells after 4 hours are _______.

Answer 1

Correct Answer: 512

To find the number of cells in a bacterial culture after 4 hours, we start with two cells, knowing the culture doubles every 30 minutes. We calculate how many doubling periods occur in 4 hours and use this to find the total cell count.

1. **Determine Doubling Periods**: Since 4 hours equals 240 minutes, and each doubling period is 30 minutes, we have:
Number of Doubling Periods = 240 / 30 = 8. 

2. **Calculate Cell Count**: The number of cells doubles every period. Therefore, after 8 periods, the number of cells is:
N = N₀ × 2ⁿ, where N₀ is the initial number of cells and n is the number of doubling periods.
Substitute the values:
N = 2 × 2⁸ = 2 × 256 = 512.

3. **Validation**: The calculated number of cells, 512, falls within the given range (512 to 512), confirming its accuracy.

Thus, the number of cells after 4 hours is 512.