Interpret a stated binary-fission population model
Calculate doubling counts and interval averages without assigning universal generation times.
Core and Extended; Biology 0610, 2026–2028. Use the stated specimen features and evidence. Diagrams are schematic. Written practice is self-checked
Before you begin
- Recall cells, DNA, inherited characteristics and the distinction between growth of an organism and production of offspring.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What happens after one complete model interval?
What you will learn
- Track completed divisions and totals
- Distinguish net increase from final count
Interpret a stated binary-fission population model
| Time / min | Total cells |
|---|---|
| 0 min | 4 |
| 40 min | 8 |
| 80 min | 16 |
| 120 min | 32 |
| 160 min | 64 |
| Feature | Meaning |
|---|---|
| Interval | 40 min only in the supplied model |
| Four doublings | 4 × 2⁴ = 64 cells |
| Net increase | 64 − 4 = 60 cells |
| Limit | No universal generation time or indefinite-growth claim |
Track completed divisions and totals
The invented count model starts with four bacterial cells. Every cell completes one binary fission during each stated 40-minute interval, with no death or movement into or out of the group. Each original becomes two daughters, so the total doubles rather than increasing by a constant four. Totals at 0, 40, 80, 120 and 160 minutes are 4, 8, 16, 32 and 64.
Four completed doubling intervals take 160 minutes and give 4 × 2⁴ = 64 cells. Net increase is 64 − 4 = 60 cells, distinct from final total. The full-interval mean net increase is 60/160 = 0.375 cells per minute. Use net change in the numerator when a rate of increase is requested, and retain the time unit from the supplied record.
Distinguish net increase from final count
The successive 40-minute increases are 4, 8, 16 and 32 cells. Their interval-average rates are 0.1, 0.2, 0.4 and 0.8 cells per minute. Thus the model does not have a constant absolute growth rate even though the doubling interval is fixed. A constant multiplication factor and a constant added count are different patterns; check the differences before describing a graph.
These clean data illustrate reproduction and counting rather than a universal bacterial growth rule. Real populations depend on species, nutrients, temperature, space, death and other conditions. No pathogen culture is assigned. Use the stated assumptions and time intervals; do not extend unrestricted doubling indefinitely or treat the model as a clinical threshold.
Pause and explain
What is the net increase from 4 to 64?
Worked example
Four bacteria undergo three complete doublings with no death. Find total and net increase.
Show the worked solution
- 4→8→16→32.
- Subtract the starting four.
Answer 32 cells in total; net increase 28 cells.
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Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the total after four completed doublings from four cells.
Give me a hint
Apply four factors of two.
Compare my reasoning
- 4→8→16→32→64.
- Do not add unchanged parents.
64 cells.
Look for these in your work
- Use four doublings
- Count daughters without extra parents
Calculate the full-interval mean net increase per minute over 160 minutes.
Give me a hint
Subtract initial count before dividing.
Compare my reasoning
- 64−4 = 60 cells.
- 60/160 = 0.375 cells/min.
0.375 cells/min, using the net increase of 60 cells.
Look for these in your work
- Use net change
- Retain rate units
Does this prove constant absolute growth or a universal bacterial 40-minute generation time?
Give me a hint
Compare added counts and retain assumptions.
Compare my reasoning
- The added counts rise: 4, 8, 16 and 32.
- The time interval is stipulated for this model.
No. Absolute interval rates increase as the population doubles, and the stated 40-minute interval is not a universal bacterial generation time.
Look for these in your work
- Distinguish factors and differences
- State model limits
Common mistakes
- Adding four after every interval.
- Using final total as net increase.
What can you explain now?
What is the net increase from 4 to 64?
Compare with the explanation
60 cells
Subtract initial from final.
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Make it stick
Calculate a doubling total and net increase, then distinguish a constant factor from a constant added count.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.