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5.5 Resource Management
Section 5.6
Resource Management
Examples
25.5 Resource Management
I see how the fish animation is an example of recursion
1. Absolutely
2. Sort of
3. Not a clue
Explain:
0 of 30
35.5 Resource Management
40%
of fish last year
1500 - + =700
at end of last year
?Fish this
year
Fish last year
Fish Population
45.5 Resource Management
Which graph best describes the fish population “in the long run”?
0% 0% 0%0%
100%
1.
2.
3.
4.
5.
# Fish
Years
# Fish
Years
# Fish
Years
# Fish
Years
# Fish
Years
55.5 Resource Management
100%
0% 0%0%0%
1. 1220
2. 1600
3. 1660
4. 1696
5. 1700
40%1500 - + =700 ?fish 2 years later
fish last year
…of fishlast year
end of last year
65.5 Resource Management
0% 0% 0%0%
100%1. 0
2. 1748
3. 1749
4. 1750
5. 3500
40%1500 - + =700 ?fish 20 years later
fish last year
…of fishlast year
end of last year
75.5 Resource Management
750
1400
1750
2000
2500
0%
100%
0%0%0%
1. 750
2. 1400
3. 1750
4. 2000
5. 2500
50%3000 - + =1000
?fish in
20 years
fish last year
…of fishlast year
at end of last year
85.5 Resource Management
Rule 1
Populations of this sort .
We call this number the . of the population
95.5 Resource Management
0%
100%
0%0%0%
1. 0
2. 1,000
3. 1,999
4. 2,000
5. 15,500
50%500 - + =1000 ?
in the long run
fish last year
…of fish
last yearend of last year
105.5 Resource Management
Rule 2
If you change only the , the population always .
.
Graphs
115.5 Resource Management
% taken out
Population now
- + =Number
added
This is irrelevant
Population next
year
125.5 Resource Management
Comparison of Models
• Compound interest and retirement funds: exponential .
• Paying credit cards: exponential .
• Resource management: .
135.5 Resource Management
S = Stabilized populationP = Percentage removed in a yearR = Number Restocked at end of a year
a.
b. c
.
None
of the
ab.
..
0%
100%
0%0%
1. a.
2. b.
3. c.
4. None of the above
Which formula describes the relationship between S, P, and R?a. P*S = R b. P*R = S c. R*S = P
145.5 Resource Management
Deer Reduction
3% 27%
33%
48%
0% 0%
100%
0%
1. 3%
2. 27%
3. 33%
4. 48%
DEP Announces Deer Reduction at Bluff Point in
Groton
150 - +?deer last year
=40 120…% of deer
removed
at end of year
in the long run
155.5 Resource Management
Logging (1)
120
tree
s
800
tree
s
100
0 tre
es
120
0 tre
es
140
0 tre
es
0%
100%
0%0%0%
1. 120 trees
2. 800 trees
3. 1000 trees
4. 1200 trees
5. 1400 trees
12%of
trees
- + =? 10,000
Trees last year add
…in the
long run
165.5 Resource Management
Logging (2)
500
750
1000
1250
1000
0
0%
100%
0%0%0%
1. 500
2. 750
3. 1,000
4. 1,250
5. 10,000
After 3 years a fire destroys half the forest. You continue to cut 12% of the trees annually. You add
trees each yearWhat will be the stabilizing value of the forest?
175.5 Resource Management
Henry is the sole inheritor of his father’s estate. He doesn’t know its current value, but he does know that his father withdraws 20% of it annually. Then at the end of the year he adds $300,000 to the estate.
$60,000 $150,000 $240,000 $1,500,000 $3,000,000
0% 0% 0%0%
100%
1. $60,000
2. $150,000
3. $240,000
4. $1,500,000
5. $3,000,000
How much can Henry expect to receive “in the long run”?
5.5 Resource Management
End of 5.6
195.5 Resource Management
Resource Management
205.5 Resource Management
“Fish Population”
Fish now =
+
-
Fish at start of last year
40% of fish
during last year
700 at end of last year
Game Warden
215.5 Resource Management
Years
Initial populatio
n
2000
500
3000
1500
Take out 50%
Add 1000
5.5 Resource Management
Meta - Material
