72. The doubling time (in minutes) of a bacterium with a specific growth rate of 2.3 h−1 in 500 ml
of growth medium is ____
Calculate Bacterial Doubling Time from Specific Growth Rate
Doubling time indicates how quickly a bacterial population doubles under
exponential growth. For a specific growth rate of
2.3 h−1, the doubling time is
18 minutes.
Doubling Time Formula
Doubling time (td) relates to the specific growth rate
(μ) by:
td = ln(2) / μ (where ln 2 ≈ 0.693)
Here, μ = 2.3 per hour. Converting to per minute:
μ = 2.3 / 60 = 0.03833 min−1
Applying the formula:
td = 0.693 / 0.03833 ≈ 18.07 minutes
This is typically rounded to 18 minutes.
The 500 ml medium volume does not affect this calculation,
as the specific growth rate is an intrinsic property of the bacterium under
ideal conditions.
Step-by-Step Calculation
- Convert units:
μmin = 2.3 / 60 = 0.03833 min−1 - Apply formula:
td = 0.693147 / 0.03833 ≈ 18.08 minutes - Direct hourly method: td = 0.693 / 2.3 ≈ 0.301 hours
0.301 × 60 = 18.06 minutes
Both methods confirm the same result.
Common Exam Options Explained
- 15 minutes:
Assumes μ = 0.693 / 0.25 = 2.772 h−1, faster than the given value. - 18 minutes:
Correct answer, matches precise calculation for μ = 2.3 h−1. - 20 minutes:
Corresponds to μ ≈ 2.079 h−1, indicating slower growth. - 30 minutes:
Corresponds to μ = 1.386 h−1, much slower growth.
