When does a population explode in a J-shaped curve, and when does it level off in an S?
Topic 3.4 Population Growth and Resource Availability: compare exponential (J-curve) and logistic (S-curve) growth, link them to r- and K-selected species, and calculate growth rate and doubling time.
A focused answer to APES Topic 3.4, covering exponential and logistic growth, r- and K-selected species, the role of resource availability, and quantitative growth-rate and rule-of-70 doubling-time calculations, with worked math.
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What this topic is asking
The College Board (Topic 3.4) wants you to compare exponential and logistic growth, link these to r- and K-selected species, and calculate growth rates and doubling times. This is a quantitative topic; expect the rule of 70.
Two growth curves
Real populations grow exponentially only while resources are abundant (for example a species newly arriving in rich, empty habitat). As numbers rise, resources become limiting and growth becomes logistic.
r- and K-selected species
The letters come from the logistic model: r is the intrinsic growth rate, K the carrying capacity. r-strategists maximize r; K-strategists are adapted to live at K. Most real species lie somewhere on a spectrum between the two extremes rather than being purely one or the other, and a species' position on that spectrum predicts how its population will respond to disturbance: r-strategists recolonise and rebound quickly after a crash, while K-strategists recover slowly but hold steady in stable conditions.
Resource availability
When resources are plentiful, birth rates exceed death rates and the population grows. As the population grows, density-dependent factors (competition, disease, waste) intensify, raising death rates and lowering birth rates until growth stops near K. This is why abundant resources allow exponential bursts but scarce resources force a logistic levelling.
The quantitative toolkit
The rule of 70 is a fast estimate: a 1% growth rate doubles in about 70 units of time, 2% in 35, 7% in 10.
Try this
Q1. Identify the shape of the curve produced by logistic growth. [1 point]
- Cue. An S-shaped (sigmoid) curve that levels off at the carrying capacity.
Q2. Calculate the doubling time of a population growing at 5% per year using the rule of 70. [1 point]
- Cue. years.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2022 (style)4 marksSection II (FRQ, quantitative). A bacterial culture of 2,000 cells grows exponentially at 8% per hour. (a) Describe the difference between exponential and logistic growth. (b) Calculate the doubling time of the bacterial population using the rule of 70. (c) Explain what eventually causes exponential growth to slow in a real population. (d) Identify whether bacteria are r-selected or K-selected and give one reason.Show worked answer →
A 4-point quantitative FRQ on population growth.
(a) Describe (1 point): exponential growth is unlimited, J-shaped growth at a constant percentage rate; logistic growth is S-shaped, slowing as the population nears the carrying capacity.
(b) Calculate (1 point): rule of 70 gives doubling time hours.
(c) Explain (1 point): resources (food, space) become limiting and density-dependent factors (competition, disease, waste) raise death rates and lower birth rates, slowing growth toward K.
(d) Identify (1 point): r-selected, because bacteria reproduce very rapidly, produce many offspring and give no parental care.
Markers reward the J-versus-S contrast, the correct rule-of-70 division, resource limitation as the brake, and r-selection justified by fast reproduction.
AP 2020 (style)1 marksSection I (multiple choice). A country's population grows at 2% per year. Using the rule of 70, approximately how many years will it take to double? (A) 14 years (B) 35 years (C) 70 years (D) 140 years. Justify your choice.Show worked answer →
A 1-point quantitative MCQ. The answer is (B).
The rule of 70 gives doubling time years. Option (A) divides by 5, (C) ignores the rate, and (D) doubles the correct answer. The trap is forgetting to divide 70 by the percentage growth rate; you do not multiply.
Related dot points
- Topic 3.3 Carrying Capacity: define carrying capacity, explain overshoot and dieback, and interpret population oscillations around the carrying capacity.
A focused answer to APES Topic 3.3, covering the definition of carrying capacity, limiting factors, overshoot and dieback, oscillation around K, and the difference between density-dependent and density-independent factors, with a worked overshoot calculation.
- Topic 3.2 Survivorship Curves: interpret Type I, II and III survivorship curves and link each shape to a species' reproductive and life-history strategy.
A focused answer to APES Topic 3.2, covering Type I, II and III survivorship curves, how each is read on a log scale, the species each describes, and how curve shape links to r- and K-selected strategies, with a worked curve-reading question.
- Topic 3.1 Generalist and Specialist Species: distinguish generalist from specialist species and explain how a changing or stable environment favors each.
A focused answer to APES Topic 3.1, covering the difference between generalist and specialist species, the role of niche breadth, and how stable versus changing environments favor each strategy, with a worked species-comparison question.
- Topic 3.7 Human Population Dynamics: explain the factors that influence human population size and growth, and calculate growth rate from crude birth, death and migration rates.
A focused answer to APES Topic 3.7, covering crude birth and death rates, immigration and emigration, the factors driving human population change, infant mortality and life expectancy, and how to calculate population growth rate, with worked math.
- Topic 3.6 Total Fertility Rate: define total fertility rate and replacement-level fertility, and explain the factors that raise or lower a country's TFR.
A focused answer to APES Topic 3.6, covering total fertility rate, replacement-level fertility, the factors that change TFR (education, family planning, infant mortality, urbanization), and its link to population growth, with a worked replacement calculation.
Sources & how we know this
- AP Environmental Science Course and Exam Description — College Board (2020)