Q85. The generation time of E. coli is 30 minutes. For an exponentially growing
culture, the initial number of bacteria required to reach a number of 109 in
2 hours is_________×107 (round off to two decimal places).
The initial number of E. coli bacteria required is 6.25 × 107.
Problem Breakdown
Exponential growth follows N = N0 × 2t/g, where N = 109 (final count), t = 2 hours (time), and g = 0.5 hours (generation time). This yields 4 generations in 2 hours, since t/g = 4. Rearranging gives N0 = 109 / 24 = 109 / 16 = 6.25 × 107.
Step-by-Step Solution
Calculate generations: 2 / 0.5 = 4. Each generation doubles the population, so from N0 to 16 × N0 = 109. Thus, N0 = 109 / 16 = 62,500,000 = 6.25 × 107. Rounded to two decimal places, the value is 6.25.
E coli generation time 30 minutes is key for exponential growth calculations in microbiology and CSIR NET life sciences prep. This article details solving: “The generation time of E. coli is 30 minutes. For an exponentially growing culture, the initial number of bacteria required to reach a number of 109 in 2 hours is_________×107 (round off to two decimal places).”
Core Formula
Use Nt = N0 × 2n, where n = t/g. Here, t = 120 minutes, g = 30 minutes, so n = 4. Then N0 = 109 / 16 = 6.25 × 107.
Verification Steps
- Time in generations: 4 doublings double population 16-fold.
- 109 / 16 = 62,500,000.
- Divided by 107: 6.25 (two decimals).
No options provided, but this matches standard binary fission math for E. coli. For CSIR NET, recognize 30-minute g as given, ignoring natural 20-minute rates.
