SME
Grade 9 Science · Problem type
Births, deaths and migration
Use this for “A herd of 500 deer has 90 births, 40 deaths, 10 arrivals and 20 departures in a year. What is its new size?”
Chart
N₁ = N + B − D + I − E
500 + 90 − 40 + 10 − 20 = 540
The flows in add and the flows out take away: N₁ = 540.
This is an example. Type your own values to start a new problem.
N₁
=
N
+
B
−
D
+
I
−
E
ΔN
Change in population
worked out (not typed)
r
Per-capita growth rate
worked out (not typed) · %
Formulas
ΔN
=
B
−
D
+
I
−
E
40 = 90 − 40 + 10 − 20
N₁
=
N
+
ΔN
540 = 500 + 40
r
=
100
×
B
−
D
N
10
=
100
×
90 − 40
500
Assumptions
•
Births and immigrants add to a population; deaths and emigrants take away.
•
The per-capita growth rate counts births minus deaths for each individual, as a percent.
•
All four counts are over the same time, here one year.
Step-by-step
WE KNOW
N = 500, B = 90, D = 40, I = 10, E = 20
FIND
change in population (ΔN), population a year later (N₁), per-capita growth rate (r)
Step 1 · Find change in population (ΔN)
Use ΔN = B − D + I − E
Births and immigrants come in; deaths and emigrants go out.
ΔN = 90 − 40 + 10 − 20
ΔN = 40
Step 2 · Find population a year later (N₁)
Use N₁ = N + ΔN
Add the change to the starting population.
N₁
=
500
+
40
N₁
=
540
Step 3 · Find per-capita growth rate (r)
Use r = 100 × (B − D) ÷ N
Births minus deaths for each individual at the start, as a percent.
r
=
100
×
90 − 40
500
r
=
100
×
50
500
r
=
5,000
500
r
=
10%
Check
Put the numbers back in. Both sides should match.
40 = 90 − 40 + 10 − 20 ✓
540 = 500 + 40 ✓
10
=
100
×
90 − 40
500
✓
Topic check
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