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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "restart; with(plots)
:\n# K\374rbis Aufgabe, siehe logistisches Wachstum, Aufgaben\n" }
{TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}
{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r
edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "G:=4000:\nkG
:=5/100:\nk:=kG/G;\na:=19:   #  f\374r eine Funktionenschar  #a:=19: \+
\nf:=x->G*exp(kG*x)/(a+exp(kG*x));\n" }}{PARA 0 "" 0 "" {TEXT -1 21 " \+
    erste Ableitung:" }{MPLTEXT 1 0 42 "\n  f1:=unapply(simplify(diff(
f(x),x)),x);\n" }}{PARA 0 "" 0 "" {TEXT -1 22 "     zweite Ableitung:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "f2:=unapply(simplify(diff(f1(x
),x)),x);\nSaettigungsgrenze:=limit(f(x),x=infinity);   # muss nat\374
rlich G sein" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG#\"\"\"\"&++)" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arro
wGF(*(%\"GG\"\"\"-%$expG6#*&%#kGGF.9$F.F.,&%\"aGF.F/F.!\"\"F(F(F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"xG6\"6$%)operatorG%&arrow
GF(,$*(\"%+Q\"\"\"-%$expG6#,$*&#F/\"#?F/9$F/F/F/,&\"#>F/F0F/!\"#F/F(F(
F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2Gf*6#%\"xG6\"6$%)operatorG%
&arrowGF(,$**\"$!>\"\"\"-%$expG6#,$*&#F/\"#?F/9$F/F/F/,&\"#>!\"\"F0F/F
/,&F9F/F0F/!\"$F:F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%2Saettigu
ngsgrenzeG\"%+S" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "\nAnfang
sbestand:=f(0);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/Anfangsbestand
G\"$+#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Wendestelle:=solv
e(f2(x)=0,x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,WendestelleG,$*&
\"#?\"\"\"-%#lnG6#\"#>F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "   \+
  maximale Wachstumsgeschwindigkeit:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 152 "maxWachstum:=f1(Wendestelle);\nZunahme_an_der_Stelle_maxWachstu
ms_Stunde:=maxWachstum/24.;\nZunahme_an_der_Stelle_maxWachstums_Stunde
:=f(50.+1/24)-f(50.);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "Zunahme_a
n_der_Stelle_maxWachstums_Stunde:=f(50.+1/48)-f(50.-1/48);\nGewicht_na
ch_einem_Monat:=f(30.);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%,maxWachstumG\"#]" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%JZunahme_an_der_Stelle_maxWachstums_StundeG$\"+MLL$3#
!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%JZunahme_an_der_Stelle_maxWa
chstums_StundeG$\"(,U)>!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%JZuna
hme_an_der_Stelle_maxWachstums_StundeG$\"([P)>!\"'" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%9Gewicht_nach_einem_MonatG$\"+IbNMw!\"(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(f(x),x=0..350);\n" }}{PARA 13 
"" 1 "" {GLPLOT2D 315 315 315 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"!F)$
\"$+#F)7$$\"3cLLLeR+Hw!#<$\"3ieIWe([B'G!#:7$$\"3rm;/^fpE9!#;$\"3[^_A><
szQF27$$\"3QLL3xM?t@F6$\"3C%3x_`8#)R&F27$$\"3mLLeR$fY#HF6$\"3Cz\"4\"y7
O/uF27$$\"3Om;ajOasOF6$\"3D(*=&H()4&G**F27$$\"3_L$3x;GfO%F6$\"3q[\\kWX
It7!#97$$\"37+]Pfw)Q3&F6$\"3#yU@_+_Gg\"FM7$$\"3iL$3FR-k#eF6$\"3+[)*3dZ
wo>FM7$$\"3%***\\(=(e`mlF6$\"3,![v!QTiNBFM7$$\"3,nm;HT&yK(F6$\"3;^+6?r
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**RFM7$$\"3'**\\(=s8$pp#F2$\"3Ix[$*)>%*)**RFM7$$\"3Omm\"H_A*oFF2$\"3;W
_C\"=E***RFM7$$\"3r*\\Pfe!HWGF2$\"3Qx+:e$\\***RFM7$$\"3]LLL))*yo\"HF2$
\"3%HuP?xk***RFM7$$\"3YL$eR666*HF2$\"3;qg*\\pv***RFM7$$\"31nT5g&GZ1$F2
$\"3IH]_zJ)***RFM7$$\"34++]Z`PKJF2$\"3M$33l+))***RFM7$$\"3&pm\"z*>1*4K
F2$\"33.ckg=****RFM7$$\"3MLLL=2DzKF2$\"3E%QhaC%****RFM7$$\"35+vVQk=`LF
2$\"33JJ'Q-'****RFM7$$\"34+DccB&RU$F2$\"3MFEx3s****RFM7$$\"$]$F)$\"3]_
:k\"4)****RFM-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!
Fe[l-%%VIEWG6$;F(Ffz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
54 "     Zeit in der 90 %  des Endbestandes erreicht wird:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 44 "Zeit:=solve(f(x)=0.9*Saettigungsgrenze,x);
\n\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ZeitG$\"+6FLG5!\"(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "dgl1:=g1(x)=kG*g(x)-kG/G*(g(
x))^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dgl1G/-%#g1G6#%\"xG,&*&#
\"\"\"\"#?F--%\"gGF(F-F-*&#F-\"&++)F-*$)F/\"\"#F-F-!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "dgl1:=g1(x)=1.*kG*g(x)-1.*k*(g(x))^
2;\ndgl2:=g1(x)=k*1.*(G-g(x))*g(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%%dgl1G/-%#g1G6#%\"xG,&*&$\"+++++]!#6\"\"\"-%\"gGF(F/F/*&$\"++++]7!#
9F/)F0\"\"#F/!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dgl2G/-%#g1G6
#%\"xG,$*($\"++++]7!#9\"\"\",&\"%+SF/-%\"gGF(!\"\"F/F2F/F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "Stammfunktion:=int(f(x),x=0..t);\nF
laecheninhalt:=int(4000-f(x),x=0..infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%.StammfunktionG,(*&\"&++)\"\"\"-%#lnG6#,&\"#>F(-%$exp
G6#,$*&\"#?!\"\"%\"tGF(F(F(F(F(*&\"'++;F(-F*6#\"\"#F(F4*&F'F(-F*6#\"\"
&F(F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/FlaecheninhaltG,&*&\"'++;
\"\"\"-%#lnG6#\"\"#F(F(*&\"&++)F(-F*6#\"\"&F(F(" }}}}{MARK "10" 0 }
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