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Differentialligninger 12
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En forskrift for populationens
En forskrift for populationens
11
størrelse som en funktion af
størrelse som en funktion af
12
tiden er dermed givet ved:
tiden er dermed givet ved:
13
Expression 14: "N" left parenthesis, "x" , right parenthesis equals "c" "e" Superscript, "k" "x" , Baseline left brace, "x" greater than or equal to 0 , right brace
N
x
=
c
e
k
x
x
≥
0
14
hvor populationsstørrelsen som
hvor populationsstørrelsen som
15
udgangspunkt er = N ( 0 ) =
udgangspunkt er = N ( 0 ) =
16
Expression 17: "c" equals StartAbsoluteValue, 100 , EndAbsoluteValue
c
=
1
0
0
equals
=
100
1
0
0
17
og hvor proportionalitetsfaktoren
og hvor proportionalitetsfaktoren
18
k kan bestemmes som følger:
k kan bestemmes som følger:
19
Expression 20: "c" "e" Superscript, "k" times 5 , Baseline equals 300
c
e
k
·
5
=
3
0
0
20
Expression 21: "k" equals StartFraction, ln left parenthesis, StartNestedFraction, 300 NestedOver "c" , EndNestedFraction , right parenthesis Over 5 , EndFraction
k
=
l
n
3
0
0
c
5
equals
=
0.2 1 9 7 2 2 4 5 7 7 3 4
0
.
2
1
9
7
2
2
4
5
7
7
3
4
21
Punkter og skyder
Punkter og skyder
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33
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"N" left parenthesis, "x" , right parenthesis equals 100 "e" Superscript, left parenthesis, 0.2 1 9 7 "x" , right parenthesis , Baseline
N
x
=
1
0
0
e
0
.
2
1
9
7
x
"N" prime left parenthesis, "x" , right parenthesis equals "k" "N" left parenthesis, "x" , right parenthesis
N
′
x
=
k
N
x
Start black, ( 5 ; 300 ) End black
(
5
;
3
0
0
)
( 0 ; c )
Start black, ( 2 ; 155.1 8 ) End black
(
2
;
1
5
5
.
1
8
)
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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