8. A bacterial population doubles every 2 hours. If the population size is N at this moment, what will be
the size of population after 2 days?
N * (248)
N * (224)
N4
N * (223)
Bacterial Population Doubling — Exponential Growth Model
Step-by-Step Solution
A bacterial population doubles every 2 hours, starting at size N.
After 48 hours (2 days), the population reaches N × 2²⁴,
since \( \frac{48}{2} = 24 \) doublings occur.
Exponential growth follows the equation: Nfinal = N × 2t/τ
where τ = 2 hours (doubling time) and t = 48 hours.
Therefore, the number of doublings = 48 / 2 = 24.
Thus,
Nfinal = N × 2²⁴.
Since 2²⁴ = 16,777,216, the population multiplies by over 16 million times.
This model represents binary fission in bacteria such as E. coli under ideal conditions —
a common concept in CSIR NET Life Sciences questions on microbial growth kinetics.
Option Analysis
N × 2⁴⁸: Assumes doubling per hour (48 doublings in 48 hours).
Incorrect — overestimates by a factor of 2²⁴.
N × 2²⁴: Correct, matches exactly 24 doublings in 48 hours.
N⁴: Represents only 4 doublings (8 hours). Vastly underestimates the population.
N × 2²³: Based on 23 doublings (46 hours). Slightly underestimates, missing the last 2 hours.
| Option | Doublings Assumed | Time Covered | Status |
|---|---|---|---|
| N × 2⁴⁸ | 48 | 96 hours | Incorrect |
| N × 2²⁴ | 24 | 48 hours | Correct |
| N⁴ | 2 (since 2² = 4) | 4 hours | Incorrect |
| N × 2²³ | 23 | 46 hours | Incorrect |
