Q.75 A bacterial culture contains 500 organisms / mL in the exponential growth phase at 8 am in
the morning. If you consider a generation time of 20 minutes, the total number of organisms
/ mL (round off to the nearest integer) after three hours (i.e. at 11 am in the morning) will be
_______.
Bacterial cultures in exponential growth phase double every generation time, leading to rapid population increases under ideal conditions. For this problem, starting with 500 organisms/mL and a 20-minute generation time over 3 hours, the population reaches 256,000 organisms/mL.
Growth Formula
Bacteria multiply via binary fission, modeled by Nt = N0 × 2n, where N0 is the initial count, n is generations, and Nt is the final count. Generation time is the doubling interval, here 20 minutes for species like E. coli.
Step-by-Step Calculation
Three hours equals 180 minutes; divide by 20 minutes/generation for n = 9 exact doublings. Thus, Nt = 500 × 29 = 500 × 512 = 256000. Round to nearest integer: 256000.
Understanding Exponential Growth Phase
In exponential (log) phase, bacteria divide at constant rate via binary fission, doubling per generation time without nutrient limits. E. coli often has 20-minute generation time under optimal conditions. Population follows geometric progression: 1 → 2 → 4 → 8, etc.
Verification and Common Errors
- Verification: After 1st hour (3 gens), 500 × 8 = 4000; repeat thrice totals 256000 organisms/mL (nearest integer).
- Common Errors: Using hours (yielding 23 = 8 doublings,
Nt = 4000) or forgetting to multiply by 512. Always convert time units consistently to minutes.
CSIR NET Exam Tips
Practice unit conversions and exact doublings; errors often stem from hours vs. minutes. Use logs for non-integer n: n = t × log(2)/g, but here integer simplifies. Relate to growth curves: lag → exponential → stationary.
