Expression 20: "f" left parenthesis, "x" , right parenthesis equals "C" "e" Superscript, negative "H" left parenthesis, "x" , right parenthesis , Baselinefx=Ce−Hx
20
Befolkningstal i millioner:
21
Expression 22: StartFraction, "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis Over 10 to the 6th power , EndFractionfx1106
equals=
163.1 3 6 5 8 8 9 1 5163.136588915
22
Expression 23: "x" Subscript, 1 , Baseline equals 17x1=17
00
5050
23
Notabene
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24
Efter 30 år er befolkningstallet
25
steget fra godt 100 millioner:
26
Expression 27: "N" left parenthesis, 0 , right parenthesisN0
equals=
113000000113000000
27
til knap 200 millioner:
28
Expression 29: "N" left parenthesis, 30 , right parenthesisN30
equals=
199814176.8 1 2199814176.812
29
Hjælpelinje og punkter
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30
Expression 31: left parenthesis, 30 , 0 plus left parenthesis, "f" left parenthesis, 30 , right parenthesis minus 0 , right parenthesis "t" , right parenthesis30,0+f30−0t
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
31
${c} mio. efter 30 år: left parenthesis, 30 , "f" left parenthesis, 30 , right parenthesis , right parenthesis30,f30
Label:
equals=
left parenthesis, 30 , 1.9 9 8 1 times 10 to the 8th power , right parenthesis30,1.9981×108
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${d} mio. efter 0 år: left parenthesis, 0 , "f" left parenthesis, 0 , right parenthesis , right parenthesis0,f0
Label:
equals=
left parenthesis, 0 , 1.1 3 times 10 to the 8th power , right parenthesis0,1.13×108
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${b} mio. efter ${a} år left parenthesis, "x" Subscript, 1 , Baseline , "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis , right parenthesisx1,fx1
Label:
equals=
left parenthesis, 17 , 1.6 3 1 4 times 10 to the 8th power , right parenthesis17,1.6314×108
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Expression 35: "a" equals "x" Subscript, 1 , Baselinea=x1
equals=
1717
35
Expression 36: "b" equals StartFraction, round left parenthesis, StartNestedFraction, "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis NestedOver 10 cubed , EndNestedFraction , right parenthesis Over 10 cubed , EndFractionb=roundfx1103103
equals=
163.1 3 7163.137
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Expression 37: "c" equals StartFraction, round left parenthesis, StartNestedFraction, "f" left parenthesis, 30 , right parenthesis NestedOver 10 cubed , EndNestedFraction , right parenthesis Over 10 cubed , EndFractionc=roundf30103103
equals=
199.8 1 4199.814
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Expression 38: "d" equals StartFraction, round left parenthesis, StartNestedFraction, "f" left parenthesis, 0 , right parenthesis NestedOver 10 cubed , EndNestedFraction , right parenthesis Over 10 cubed , EndFractiond=roundf0103103
equals=
113113
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`N\left(x\right)=\frac{\int_0^xe^{H\left(t\right)}\cdot g\left(t\right)\ dt+C}{e^{H\left(x\right)}}` left parenthesis, 3 , 2.6 times 10 to the 8th power , right parenthesis3,2.6·108
Label:
equals=
left parenthesis, 3 , 2.6 times 10 to the 8th power , right parenthesis3,2.6×108
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199.814 mio. efter 30 år
113 mio. efter 0 år
163.137 mio. efter 17 år
"N" left parenthesis, "x" , right parenthesis equals StartFraction, Start integral from 0 to "x" , end integral, "e" Superscript, "H" left parenthesis, "t" , right parenthesis , Baseline times "g" left parenthesis, "t" , right parenthesis "d" "t" plus "C" Over "e" Superscript, "H" left parenthesis, "x" , right parenthesis , Baseline , EndFractionNx=∫x0eHt·gtdt+CeHx