Q.65
A bacterial strain is grown in nutrient medium at 37 °C under aerobic conditions.
The medium is inoculated with 10² cells from a seed culture. If the number of
cells in the culture is 10⁵ after 10 hours of growth, the doubling time of the strain
(rounded off to nearest integer) is __________ h.

Problem Breakdown

A bacterial strain starts at N₀ = 10² cells and reaches N_t = 10⁵ after t = 10 hours at 37°C aerobically.

Exponential growth follows:

N_t = N₀ × 2ⁿ, where n is number of generations.

Here:

10⁵ = 10² × 2ⁿ ⇒ 2ⁿ = 10³ = 1000

Doubling time: T_d = t / n

Step-by-Step Solution

n = log₂(1000) = ln(1000) / ln(2) ≈ 6.907 / 0.693 ≈ 9.965

T_d = 10 / 9.965 ≈ 1.003 hours

Rounded doubling time ≈ 1 hour

Correct Answer

Doubling Time = 1 hour

Common Mistake Options Explained

• 10 hours – assumes linear growth, not exponential
• 2 hours – misreads as 5 doublings (2⁵ = 32, wrong factor)
• 1 hour (Correct) – ~10 doublings, 2¹⁰ ≈ 1000
• 20 minutes – typical for E. coli, not from calculation