Biology • Year 11 • Module 4 • Lesson 7
Population Growth — Exponential, Logistic and Carrying Capacity
Lock in the core vocabulary, the four population factors, and the key differences between J-curves and S-curves.
1. Label the population growth curves
The diagram below shows two population growth curves plotted against the same axes. Write the missing labels into boxes A–H. Each label is drawn from the lesson’s Key Terms or Content Cards 2–3. 8 marks
Schematic growth curves. Not drawn to scale.
| Label | Your answer |
|---|---|
| A | |
| B | |
| C | |
| D | |
| E | |
| F | |
| G | |
| H |
2. Term–definition match
The ten definitions below are shuffled. In the right-hand column write the matching term from this list: population, natality, mortality, immigration, emigration, exponential growth, logistic growth, carrying capacity (K), density-dependent factor, density-independent factor. 10 marks
| # | Definition (shuffled) | Matching term |
|---|---|---|
| 2.1 | All organisms of the same species living in a defined area at a given time. | |
| 2.2 | The birth rate; the number of new individuals added to a population per unit time. | |
| 2.3 | The death rate; the number of individuals lost from a population per unit time. | |
| 2.4 | Individuals moving into a population from elsewhere, increasing its size. | |
| 2.5 | Individuals moving out of a population to another area, decreasing its size. | |
| 2.6 | Population growth under unlimited resource conditions, producing a J-shaped curve where the rate of increase is proportional to population size. | |
| 2.7 | Population growth when resources are limited, producing an S-shaped curve; growth slows as the population approaches K. | |
| 2.8 | The maximum population size that an environment can sustainably support, determined by available food, water, shelter and other resources. | |
| 2.9 | A limiting factor whose intensity increases as population density increases; examples include food competition, disease transmission and predation. | |
| 2.10 | A limiting factor whose effect is unrelated to population density; examples include drought, flood and wildfire. |
3. Population size formula
Use the formula Population change = (natality + immigration) − (mortality + emigration) to answer each part. 6 marks (2 each)
3.1 A population of 200 frogs has 60 births, 25 deaths, 10 immigrants and 5 emigrants in one year. What is the new population size?
3.2 A bird population of 500 records 180 births, 220 deaths, 5 immigrants and 40 emigrants. Calculate the new population size and state whether it has grown, declined or is stable.
3.3 A population is stable at 1000 individuals. Natality = 80, immigration = 20. What must mortality + emigration equal for the population to remain at 1000?
4. True or false — with correction
For each statement, circle T or F. If the statement is false, write the corrected version on the line provided. 8 marks (1 for T/F, 1 for the correction where needed)
4.1 Exponential growth produces an S-shaped curve because resources are unlimited. T / F
4.2 Carrying capacity (K) is a fixed number that never changes for a given species. T / F
4.3 Disease transmission is a density-dependent limiting factor because it spreads more easily when individuals are crowded together. T / F
4.4 A population at carrying capacity has a birth rate that is much higher than its death rate, causing the population to grow rapidly. T / F
5. Function recall
Answer each in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
5.1 Why do introduced species (like the European rabbit in Australia) commonly show exponential growth soon after arrival?
5.2 What causes a logistic growth curve to level off and form a plateau near K?
5.3 How does a wildfire act as a density-independent limiting factor?
5.4 In the logistic growth model, which phase of the S-curve shows growth most similar to exponential growth, and why does this eventually stop?
Q1 — Labelled growth curves (8 marks)
A: J-curve (exponential growth curve). B: S-curve (logistic growth curve / sigmoidal curve). C: K — carrying capacity (the maximum sustainable population size). D: Lag phase — population is small, growth is slow while individuals establish. E: Exponential phase — resources still abundant, population grows rapidly (middle section of S-curve). F: Plateau phase — population stabilises near K; birth rate ≈ death rate. G: Exponential growth — occurs when resources are unlimited (no competition, no predation, no disease). H: Resource limitation / density-dependent factors intensifying — as population grows, food, space and other resources become scarce, slowing growth.
Award 1 mark per correct label. Accept equivalent terms (e.g. “sigmoidal” for B).
Q2 — Term–definition matches (10 marks)
2.1 population • 2.2 natality • 2.3 mortality • 2.4 immigration • 2.5 emigration • 2.6 exponential growth • 2.7 logistic growth • 2.8 carrying capacity (K) • 2.9 density-dependent factor • 2.10 density-independent factor. Award 1 mark each.
Q3 — Population formula (6 marks, 2 each)
3.1 Change = (60 + 10) − (25 + 5) = 70 − 30 = +40. New population = 200 + 40 = 240. [1 mark for working, 1 mark for correct answer]
3.2 Change = (180 + 5) − (220 + 40) = 185 − 260 = −75. New population = 500 − 75 = 425. The population has declined. [1 mark for correct answer and sign; 1 mark for stating declined]
3.3 For stability, change = 0. So (natality + immigration) must equal (mortality + emigration). Natality + immigration = 80 + 20 = 100. Therefore mortality + emigration must also equal 100. [1 mark for reasoning, 1 mark for answer]
Q4 — True or false (8 marks)
4.1 False. Correction: Exponential growth produces a J-shaped curve, not an S-shaped curve. The J-curve occurs because resources are unlimited. The S-shaped curve results from logistic growth when resources are limited. [1 T/F + 1 correction]
4.2 False. Correction: Carrying capacity is not a fixed number — it changes with environmental conditions. Drought reduces K (less food and water), while good rains increase K (more vegetation). Biological control (e.g. myxomatosis) also reduced the carrying capacity for rabbits in Australia. [1 T/F + 1 correction]
4.3 True. Disease transmission increases as population density increases because individuals come into closer contact more frequently, making pathogen transmission easier. This is the definition of a density-dependent factor. [1 mark, no correction needed]
4.4 False. Correction: At carrying capacity, birth rate approximately equals death rate, so the population is stable (growth rate ≈ 0), not growing rapidly. Rapid growth occurs in the exponential or early logistic phase when resources are still abundant. [1 T/F + 1 correction]
Q5 — Function recall (8 marks, 2 each)
5.1 Introduced species show exponential growth because the new environment typically lacks the natural predators, parasites and competitors that limited the species in its original habitat. With abundant resources and few regulatory factors, all four conditions for exponential growth are met: low mortality, high natality, and minimal density-dependent regulation. [Award 1 mark for “lack of predators/disease/competitors”; 1 mark for linking this to unlimited conditions]
5.2 As the population grows, density-dependent limiting factors intensify: food competition increases, disease transmits more easily, predation pressure rises, and waste accumulates. This progressively reduces the net growth rate until birth rate ≈ death rate at K, causing the plateau. [1 mark for density-dependent factors intensifying; 1 mark for birth rate ≈ death rate at K]
5.3 A wildfire kills or displaces organisms regardless of how many individuals are present in the area; a small population and a large population in the same fire zone both suffer the same proportional or absolute destruction. Because the intensity of the factor does not increase with density, it is density-independent. [1 mark for “unrelated to density”; 1 mark for explanation]
5.4 The exponential phase (middle of the S-curve) shows the fastest growth, similar to a J-curve, because resources are still relatively abundant and density-dependent factors are not yet strong. This phase ends because resource availability decreases as the population grows larger, causing density-dependent factors to intensify and slow the growth rate. [1 mark for naming the exponential phase of the S-curve; 1 mark for resources becoming limiting]