SME
Human Geography · Problem type
Birth, death and growth rates
Use this for “A country of 500,000 had 6,000 births and 4,000 deaths. Find CBR, CDR and RNI, and its doubling time.”
Chart
12 per 1,000
8 per 1,000
This is an example. Type your own values to start a new problem.
P₀
Population
example
B
Births
example
D
Deaths
example
CBR
Crude birth rate
calculated · per 1,000
CDR
Crude death rate
calculated · per 1,000
RNI
Rate of natural increase
calculated · %
T₂
Doubling time
calculated · years
Formulas
CBR
=
B
P₀
×
1,000
12
=
6,000
500,000
×
1,000
CDR
=
D
P₀
×
1,000
8
=
4,000
500,000
×
1,000
RNI
=
CBR − CDR
10
0.4
=
12 − 8
10
T₂
≈
70
RNI
175
≈
70
0.4
Assumptions
•
Rates are per 1,000 people a year, so places of different sizes compare; P₀ is the mid-year population.
•
RNI is the birth rate minus the death rate, as a percent; it leaves out migration.
•
Rule of 70: if RNI stays the same, the population doubles in about 70 ÷ RNI years.
Step-by-step
WE KNOW
B = 6,000, D = 4,000, P₀ = 500,000
FIND
crude birth rate (CBR), crude death rate (CDR), rate of natural increase (RNI), doubling time (T₂)
Step 1 · Find crude birth rate (CBR)
Use CBR = B ÷ P₀ × 1,000
Births per person, scaled to births per 1,000 people.
CBR
=
6,000
500,000
×
1,000
CBR = 0.012 × 1,000
CBR = 12 per 1,000
Step 2 · Find crude death rate (CDR)
Use CDR = D ÷ P₀ × 1,000
Deaths per person, scaled to deaths per 1,000 people.
CDR
=
4,000
500,000
×
1,000
CDR = 0.008 × 1,000
CDR = 8 per 1,000
Step 3 · Find rate of natural increase (RNI)
Use RNI = (CBR − CDR) ÷ 10
Subtract the death rate from the birth rate; dividing by 10 turns “per 1,000” into a percent.
RNI
=
12 − 8
10
RNI
=
4
10
RNI = 0.4%
Step 4 · Find doubling time (T₂)
Use T₂ ≈ 70 ÷ RNI
Rule
of
70:
steady
growth
of
RNI%
a
year
doubles
a
population
in
about
70
RNI
years.
T₂
=
70
RNI
T₂
=
70
0.4
T₂
=
175
years
Check
Put the numbers back in. Both sides should match.
12
=
6,000
500,000
×
1,000
✓
8
=
4,000
500,000
×
1,000
✓
0.4
=
12 − 8
10
✓
175
≈
70
0.4
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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