population-dynamics Rule of 70 Tap / Space to flip
population-dynamics Doubling time (years) ≈ 70 ÷ growth rate (% per year). Example: 2% growth → doubles in 35 years.
Priority topic · Easy points
Population Dynamics
Doubling time and TFR show up on practically every released APES exam. Memorize the formulas and the four-stage demographic transition — these are the cheapest points on the test.
Core formulas
Growth rate from CBR / CDR
r% = (CBR − CDR) / 10
CBR (Crude Birth Rate) and CDR (Crude Death Rate) are usually given per 1000 people per year. Divide by 10 to get a percent.
Growth rate from raw counts
r = (births − deaths + immigrants − emigrants) / N × 100
Use this when given raw counts; remember to include migration.
Doubling time (Rule of 70)
Doubling time (yr) = 70 / r%
A country growing at 2% per year doubles in 35 years. At 1%, doubles in 70 years. Most-tested formula in APES.
Population in n doublings
N = N₀ × 2ⁿ
50 M growing at 1.4% (doubling time 50 yr) → 100 M after 50 yr; 200 M after 100 yr.
Total Fertility Rate (TFR)
- TFR = average lifetime children per woman.
- Replacement TFR ≈ 2.1 in developed nations (the 0.1 covers child mortality and same-sex births).
- Higher in nations with high infant mortality (~2.3+).
- Below replacement → population shrinks (Japan, Italy, S. Korea).
Demographic Transition Model (DTM)
| Stage | Birth rate | Death rate | Pop. growth | Example |
|---|---|---|---|---|
| 1 — Pre-industrial | High | High | Low / stable | Pre-1700 societies; almost none today |
| 2 — Transitional | High | Falling (medicine, sanitation) | Rapid | Sub-Saharan Africa today |
| 3 — Industrial | Falling (urbanization, education) | Low | Slowing | Mexico, India |
| 4 — Post-industrial | Low | Low | Stable | USA, Australia |
| 5 — Declining (emerging) | Below replacement | Low | Negative | Japan, Italy, Germany |
Stage 2 is the period of fastest growth — death rate falls before birth rate does.
Age-structure pyramids
| Shape | Indicates | Example |
|---|---|---|
| Wide base, narrow top (pyramid) | Rapid growth (many young) | Niger, Nigeria |
| Rectangular | Stable population | USA |
| Narrow base, wider middle | Decline (below-replacement TFR) | Japan, Italy |
Worked example #1: Rule of 70
A country has CBR = 32 and CDR = 12 per 1000 per year. What is the doubling time?
Step 1 · Growth rate
r% = (32 − 12) / 10 = 2.0%
Step 2 · Doubling time
Doubling time = 70 / 2.0 = 35 yearsWorked example #2: population projection
50 million people growing at 1.4% per year — population in 50 years?
Doubling time = 70 / 1.4 = 50 years
After 50 yr: 50 M × 2 = 100 M
(After 100 yr: 200 M; after 150 yr: 400 M)Worked example #3: with migration
Population 200,000. In one year: 4,000 births, 1,500 deaths, 500 immigrants, 1,000 emigrants. Growth rate?
Net change = 4000 − 1500 + 500 − 1000 = 2000
r% = (2000 / 200,000) × 100 = 1.0%Example FRQs
Long FRQ A country has 80 million people growing at 3.5% per year. (a) Doubling time? (b) Population in 40 years?
Answer:
(a) Doubling time = 70 / 3.5 = 20 years
(b) 40 years = 2 doubling periods
Population = 80 M × 2 × 2 = 320 millionFRQ Identify TWO factors that lower TFR.
Answer: Any two of: education of women, access to family planning / contraception, urbanization, low infant mortality, economic opportunity for women, government policy or incentives.
FRQ Describe ONE environmental impact of rapid population growth in a developing country and propose ONE solution.
Answer: Impact: rapid population growth drives deforestation, as land is cleared for subsistence agriculture and fuelwood. This causes habitat loss, soil erosion, and reduced carbon sequestration. Solution: invest in girls\' education and family-planning access, which historically lower TFR. Pair with sustainable-agriculture training (agroforestry, no-till) so existing farmland feeds more people without further forest clearing.
MCQ In a typical age-structure diagram, a wide base indicates: (A) An aging population (B) A stable population (C) Rapid future growth (D) Declining birth rate
Answer: C. A wide base means many young people who will reach reproductive age — strong future growth.
Drill flashcards
population-dynamics Total fertility rate (TFR) Tap / Space to flip
population-dynamics Average number of children a woman has in her lifetime. TFR = 2.1 is replacement level (developed) due to child mortality.
population-dynamics Demographic transition · Stage 1 Tap / Space to flip
population-dynamics Pre-industrial: high birth rate, high death rate, low population growth. Pre-1700s.
population-dynamics Demographic transition · Stage 2 Tap / Space to flip
population-dynamics Transitional: high birth rate, falling death rate (better food, sanitation, medicine). Population explodes.
population-dynamics Demographic transition · Stage 3 Tap / Space to flip
population-dynamics Industrial: birth rate falls (urbanization, education, contraception). Growth slows.
population-dynamics Demographic transition · Stage 4 Tap / Space to flip
population-dynamics Post-industrial: low birth rate, low death rate. Stable or declining population (Japan, Germany).
population-dynamics Age-structure pyramid · expanding Tap / Space to flip
population-dynamics Wide base, narrow top. High birth rate, young population, rapid growth (developing nations).
population-dynamics Age-structure pyramid · stable Tap / Space to flip
population-dynamics Roughly equal columns from base to upper-middle ages. Birth rate ≈ death rate. Slow / no growth.
population-dynamics Age-structure pyramid · declining Tap / Space to flip
population-dynamics Narrow base, wider middle. Below-replacement TFR. Population shrinks (Japan, Italy).
population-dynamics Infant mortality rate (IMR) Tap / Space to flip
population-dynamics Deaths per 1000 live births before age 1. High IMR correlates with high TFR (insurance behavior).