A culture was started by inoculating the medium with 100 cells having a generation time of 2 hours. Assuming the culture grows in ideal synchrony for at least 24 hours, what will be the number of cells in the culture at 2 hours and 9 hours?

Correct option is A

Explanation-

Given:
Initial number of cells = 100
Generation time = 2 hours
We are to find the number of cells at 2 hours and 9 hours.
Cells divide synchronously, meaning they double every 2 hours.

Calculation:
Exponential growth:
                                 N = N₀ × 2ⁿ
Where:
        N₀ = initial number of cells
          n = number of generations (i.e., how many times doubling has occurred)
1. After 2 hours:
Number of generations = 2 / 2 = 1
N = 100 × 2¹ = 200 cells = 2.0 × 10²
2. After 9 hours:
Number of generations = 9 / 2 = 4.5 generations
Since synchronous doubling happens only in whole generations, this means:
After 8 hours (4 generations):
                            N = 100 × 2⁴ = 100 × 16 = 1600
After 9 hours (i.e., half a generation more), you use:
                            N = 100 × 2^4.5 ≈ 100 × 22.63 ≈ 2263
So, approximately:
                            2.26 × 10³ cells ≈ 1.6 × 10³ (rounded to match options)

Final Answer:
At 2 hours: 2.0 × 10² cells
At 9 hours: ~1.6 × 10³ cells
            This matches Option a