SME
Physical Geography · Problem type
Species lost when habitat shrinks
Use this for “Only 10 % of a forest is left. With z = 0.25, what share of its species will it lose?”
Chart
s(10) ≈ 56.23
This is an example. Type your own values to start a new problem.
s
%
=
100
×
(
÷
100)
l
%
=
100
−
s
%
Formulas
s
=
100
×
(
a
100
)
z
56.2341
=
100
×
(
10
100
)
0.25
l
=
100
−
s
43.7659 = 100 − 56.2341
Assumptions
•
S = cAz holds before and after with the same c and z, so c cancels in the share kept.
•
Keeping a share of the area keeps that share to the power z of the species.
•
The loss comes over decades as small populations die out, not on the day the forest is cut.
Step-by-step
WE KNOW
a = 10%, z = 0.25
FIND
species kept (s), species lost (l)
Step 1 · Find species kept (s)
Use s = 100 × (a ÷ 100)ᶻ
Turn
the
area
kept
into
a
share,
raise
it
to
the
power
z
,
and
turn
it
back
into
a
percent.
s
=
100
×
(
10
100
)
0.25
10
100
=
0.1
0.1
0.25
=
0.5623
100 × 0.5623 = 56.23
s
=
56.2341%
Step 2 · Find species lost (l)
Use l = 100 − s
The species not kept are the ones lost in time.
l
=
100
−
56.2341
l
=
43.7659%
Check
Put the numbers back in. Both sides should match.
56.2341
=
100
×
(
10
100
)
0.25
✓
43.7659 = 100 − 56.2341 ✓
Topic check
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