Unit 3 · Topic 3.8 Beta

Human Population Dynamics

Crude birth and death rates count births and deaths per 1,000 people per year.

Practice 6: Mathematical Routines

Part 1 · Hook

Why this matters

Two countries each have 40 million people today. In one, 36 babies are born each year for every 1,000 people and 8 people die. In the other, 11 are born and 9 die. The first will have 80 million people in about 25 years; the second would take about 350 years to double. Two numbers per country, and one rule you can do in your head, tell you which is which.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. A population grows 2% a year. Using the rule of 70, what is its doubling time?

  1. 35 years
  2. 2 years
  3. 140 years
  4. 0.35 years
Show the answer

70 divided by the growth rate in percent: 70 / 2 = 35 years.

  • Correct: 35 years:
  • 2 years:
  • 140 years:
  • 0.35 years:

2. What is replacement-level fertility in a country where few children die young?

  1. About 2.1 children per woman
  2. Exactly 1 child per woman
  3. About 4 children per woman
  4. Exactly 3 children per woman
Show the answer

About 2.1, a little above 2, because some children die before adulthood.

  • Correct: About 2.1 children per woman:
  • Exactly 1 child per woman:
  • About 4 children per woman:
  • Exactly 3 children per woman:

Part 4 · See it

See it first

Line graph of a population of 10 million growing 2% a year for 105 years. Dashed guides mark doubling every 35 years: about 20 million at 35 years, 40 million at 70 years and 80 million at 105 years, as the rule of 70 predicts (70 divided by 2 is 35). Invented example.
A population of 10 million growing 2% a year doubles about every 35 years, as the rule of 70 predicts. Invented example. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Births and deaths are counted per 1,000 people per year (crude birth rate and crude death rate)their difference is the natural increase per 1,000 people per year
  2. Dividing that difference by 10 turns "per 1,000" into "per 100"the result is the rate of natural increase in percent
  3. Dividing 70 by the growth rate in percentgives the doubling time in years; adding it to the start year gives the year the population doubles
  4. Immigration adds people and emigration removes thema country’s total growth can differ from its natural increase

Part 6 · Key ideas

Key ideas

  • Crude birth rate (CBR): births per 1,000 people per year. Crude death rate (CDR): deaths per 1,000 people per year.
  • Rate of natural increase (in %) =CBR−CDR10= \frac{\text{CBR} - \text{CDR}}{10}. The 10 turns a rate per 1,000 into a percent (per 100).
  • Doubling time (years) =70growth rate in %= \frac{70}{\text{growth rate in }\%}. For "in what year", add the doubling time to the start year.
  • Total growth also counts immigration (people moving in) and emigration (people moving out). Malthusian theory holds that population grows faster than food, so famine, disease or war will check it.

Part 7 · Misconception

A common mistake

The wrong idea: A crude birth rate of 36 and a crude death rate of 8 mean the population grows 28% a year.

What actually happens: Both rates are per 1,000 people, so the gap of 28 per 1,000 is 2.8 per 100: a growth rate of 2.8% a year. Divide by 10, not 100, and do not leave it at 28.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data

Birth and death rates in four countries

Crude birth rate and crude death rate, per 1,000 people per year, 2025 (invented data for practice)
CountryCrude birth rateCrude death rate
Country J368
Country K227
Country L119
Country M811

1. Which country in the table has the highest rate of natural increase?

  1. Country J
  2. Country K
  3. Country L
  4. Country M
Show the answer

The rate of natural increase depends on the gap between the birth and death rates, not on either one alone.

  • Correct: Country J: Right: 36 - 8 = 28 per 1,000, the largest gap, which is 2.8%.
  • Country K: K’s gap is 22 - 7 = 15 per 1,000, or 1.5%.
  • Country L: L’s gap is 11 - 9 = 2 per 1,000, or 0.2%.
  • Country M: M has more deaths than births: 8 - 11 = -3 per 1,000.

2. What is Country K’s rate of natural increase, in percent?

Type a number, then its unit (%). Scale words (2.5 million) and powers of ten (2.5 × 10^6) are read.

Show the answer

22−710=1.5%\frac{22 - 7}{10} = 1.5\% a year. The difference is per 1,000 people; dividing by 10 makes it per 100, a percent.

  • Answer: 1.5 %

3. Country J’s rate of natural increase is 2.8%. Write the setup for its doubling time by the rule of 70, then give the answer with its unit.

Type the setup as on the exam, with brackets and units, then the answer.

Show the answer

702.8=25\frac{70}{2.8} = 25 years.

  • Setup: 702.8\frac{70}{2.8}; answer 25 yr

4. Country J had 40 million people in 2025. If its rate of natural increase stays at 2.8% and no one moves in or out, in what year will it have about 80 million people?

Type a number. Scale words (2.5 million) and powers of ten (2.5 × 10^6) are read.

Show the answer

Doubling time 702.8=25\frac{70}{2.8} = 25 years, so 2025+25=20502025 + 25 = 2050. The question asks for a year, so add the doubling time to the start year.

  • Answer: 2050

5. What does a crude death rate of 9 mean?

  1. 9% of people die each year
  2. 9 deaths per 1,000 people per year
  3. 9 deaths per woman over her lifetime
  4. 9 deaths per 100 people per year
Show the answer

Crude rates are per 1,000 people per year.

  • 9% of people die each year: 9% would be 90 per 1,000, ten times more.
  • Correct: 9 deaths per 1,000 people per year: Right: crude rates count per 1,000 people per year.
  • 9 deaths per woman over her lifetime: Rates per woman describe fertility, not deaths.
  • 9 deaths per 100 people per year: Per 100 is a percent; crude rates are per 1,000.

6. Explain how a country’s population can grow even though its crude death rate is higher than its crude birth rate.

Build the answer part by part, then write it in your own words.

Show the answer

Natural decrease, outweighed by net immigration.

  • An answer that earns the point: Its natural increase is negative, because deaths outnumber births, but more people move in than move out, so net immigration adds more people than natural decrease removes and the population grows.

7. Which changes would raise a country’s total population growth rate, if nothing else changes? Select all that apply.

  1. The crude death rate falls while births stay the same
  2. Both crude rates fall by 2 per 1,000
  3. The crude birth rate falls
  4. More people emigrate
Show the answer

Growth rises with more births or immigrants and with fewer deaths or emigrants. A fall in births that matches a fall in deaths leaves the gap unchanged.

  • Correct: The crude death rate falls while births stay the same: Right: fewer deaths widen the gap between births and deaths.
  • Both crude rates fall by 2 per 1,000: If births and deaths both fall by 2 per 1,000, the gap, and so the growth rate, stays the same.
  • The crude birth rate falls: Fewer births lower the growth rate.
  • More people emigrate: Emigrants leave, lowering the growth rate.

Part 9 · Summary

Summary

Crude birth and death rates count births and deaths per 1,000 people per year. Their difference divided by 10 is the rate of natural increase in percent, and 70 divided by that rate is the doubling time in years; add it to the start year to find the year a population doubles. Immigration and emigration also change population size. Malthus argued that population would outrun food; so far, food production has kept pace, but his question about limits remains.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

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