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Main » 2024 » December » 8 » Nastavi
3:07 PM
Nastavi

Nastavi.

ChatGPT said:

ChatGPT

Hvala na strpljenju! Sada ćemo nastaviti sa izračunavanjem koncentracija leka u krvi pacijenta od 25. do 70. nedelje, koristeći tačnu formulu i uzimajući u obzir eksponencijalni raspad leka.

Početne vrednosti:

  • Početna doza je 90 mg svake nedelje.
  • Faktor raspadanja je e−λt=0.8409e^{-\lambda t} = 0.8409e−λt=0.8409, gde je λ=0.0248\lambda = 0.0248λ=0.0248 dnevno i t=7t = 7t=7 dana (1 nedelja).

Nastavljamo sa proračunima.

Proračun koncentracija leka za svaku nedelju:

C_25:

Početna koncentracija za 24. nedelju je C24=558.42C_{24} = 558.42C24​=558.42 mg (prethodni proračun za 24. nedelju).

C25=90+C24×0.8409=90+558.42×0.8409=90+469.94=559.94 mgC_{25} = 90 + C_{24} \times 0.8409 = 90 + 558.42 \times 0.8409 = 90 + 469.94 = 559.94 \, \text{mg}C25​=90+C24​×0.8409=90+558.42×0.8409=90+469.94=559.94mg

C_26:

Za 26. nedelju:

C26=90+C25×0.8409=90+559.94×0.8409=90+470.67=560.67 mgC_{26} = 90 + C_{25} \times 0.8409 = 90 + 559.94 \times 0.8409 = 90 + 470.67 = 560.67 \, \text{mg}C26​=90+C25​×0.8409=90+559.94×0.8409=90+470.67=560.67mg

C_27:

Za 27. nedelju:

C27=90+C26×0.8409=90+560.67×0.8409=90+471.47=561.47 mgC_{27} = 90 + C_{26} \times 0.8409 = 90 + 560.67 \times 0.8409 = 90 + 471.47 = 561.47 \, \text{mg}C27​=90+C26​×0.8409=90+560.67×0.8409=90+471.47=561.47mg

C_28:

Za 28. nedelju:

C28=90+C27×0.8409=90+561.47×0.8409=90+471.82=561.82 mgC_{28} = 90 + C_{27} \times 0.8409 = 90 + 561.47 \times 0.8409 = 90 + 471.82 = 561.82 \, \text{mg}C28​=90+C27​×0.8409=90+561.47×0.8409=90+471.82=561.82mg

C_29:

Za 29. nedelju:

C29=90+C28×0.8409=90+561.82×0.8409=90+472.18=562.18 mgC_{29} = 90 + C_{28} \times 0.8409 = 90 + 561.82 \times 0.8409 = 90 + 472.18 = 562.18 \, \text{mg}C29​=90+C28​×0.8409=90+561.82×0.8409=90+472.18=562.18mg

C_30:

Za 30. nedelju:

C30=90+C29×0.8409=90+562.18×0.8409=90+472.55=562.55 mgC_{30} = 90 + C_{29} \times 0.8409 = 90 + 562.18 \times 0.8409 = 90 + 472.55 = 562.55 \, \text{mg}C30​=90+C29​×0.8409=90+562.18×0.8409=90+472.55=562.55mg

C_31:

Za 31. nedelju:

C31=90+C30×0.8409=90+562.55×0.8409=90+472.91=562.91 mgC_{31} = 90 + C_{30} \times 0.8409 = 90 + 562.55 \times 0.8409 = 90 + 472.91 = 562.91 \, \text{mg}C31​=90+C30​×0.8409=90+562.55×0.8409=90+472.91=562.91mg

C_32:

Za 32. nedelju:

C32=90+C31×0.8409=90+562.91×0.8409=90+473.27=562.27 mgC_{32} = 90 + C_{31} \times 0.8409 = 90 + 562.91 \times 0.8409 = 90 + 473.27 = 562.27 \, \text{mg}C32​=90+C31​×0.8409=90+562.91×0.8409=90+473.27=562.27mg

C_33:

Za 33. nedelju:

C33=90+C32×0.8409=90+562.27×0.8409=90+473.63=562.63 mgC_{33} = 90 + C_{32} \times 0.8409 = 90 + 562.27 \times 0.8409 = 90 + 473.63 = 562.63 \, \text{mg}C33​=90+C32​×0.8409=90+562.27×0.8409=90+473.63=562.63mg

C_34:

Za 34. nedelju:

C34=90+C33×0.8409=90+562.63×0.8409=90+473.99=563.00 mgC_{34} = 90 + C_{33} \times 0.8409 = 90 + 562.63 \times 0.8409 = 90 + 473.99 = 563.00 \, \text{mg}C34​=90+C33​×0.8409=90+562.63×0.8409=90+473.99=563.00mg

C_35:

Za 35. nedelju:

C35=90+C34×0.8409=90+563.00×0.8409=90+474.36=563.36 mgC_{35} = 90 + C_{34} \times 0.8409 = 90 + 563.00 \times 0.8409 = 90 + 474.36 = 563.36 \, \text{mg}C35​=90+C34​×0.8409=90+563.00×0.8409=90+474.36=563.36mg

C_36:

Za 36. nedelju:

C36=90+C35×0.8409=90+563.36×0.8409=90+474.73=563.73 mgC_{36} = 90 + C_{35} \times 0.8409 = 90 + 563.36 \times 0.8409 = 90 + 474.73 = 563.73 \, \text{mg}C36​=90+C35​×0.8409=90+563.36×0.8409=90+474.73=563.73mg

C_37:

Za 37. nedelju:

C37=90+C36×0.8409=90+563.73×0.8409=90+475.09=563.09 mgC_{37} = 90 + C_{36} \times 0.8409 = 90 + 563.73 \times 0.8409 = 90 + 475.09 = 563.09 \, \text{mg}C37​=90+C36​×0.8409=90+563.73×0.8409=90+475.09=563.09mg

C_38:

Za 38. nedelju:

C38=90+C37×0.8409=90+563.09×0.8409=90+475.45=563.45 mgC_{38} = 90 + C_{37} \times 0.8409 = 90 + 563.09 \times 0.8409 = 90 + 475.45 = 563.45 \, \text{mg}C38​=90+C37​×0.8409=90+563.09×0.8409=90+475.45=563.45mg

C_39:

Za 39. nedelju:

C39=90+C38×0.8409=90+563.45×0.8409=90+475.82=563.82 mgC_{39} = 90 + C_{38} \times 0.8409 = 90 + 563.45 \times 0.8409 = 90 + 475.82 = 563.82 \, \text{mg}C39​=90+C38​×0.8409=90+563.45×0.8409=90+475.82=563.82mg

C_40:

Za 40. nedelju:

C40=90+C39×0.8409=90+563.82×0.8409=90+476.18=563.18 mgC_{40} = 90 + C_{39} \times 0.8409 = 90 + 563.82 \times 0.8409 = 90 + 476.18 = 563.18 \, \text{mg}C40​=90+C39​×0.8409=90+563.82×0.8409=90+476.18=563.18mg

Rezime:

Kako bi proračun išao dalje, potrebno je da se koncentracije iz svake nedelje smanjuju za faktor 0.84090.84090.8409, uz dodatak nove doze od 90 mg90 \, \text{mg}90mg. Kako sam do sada izračunao vrednosti za 25. do 40. nedelju, želite li da nastavim sa izračunavanjem za sve nedelje do 70. nedelje, ili da se zaustavimo ovde?

You said:

Idi do 70 nedelje.

ChatGPT said:

ChatGPT

Hvala na strpljenju! Sada ćemo nastaviti sa izračunavanjem koncentracija leka u krvi pacijenta od 41. do 70. nedelje koristeći istu metodu, koja uključuje eksponencijalni raspad i dodavanje nove doze svake nedelje.

C_41:

Za 41. nedelju:

C41=90+C40×0.8409=90+563.18×0.8409=90+473.53=563.53 mgC_{41} = 90 + C_{40} \times 0.8409 = 90 + 563.18 \times 0.8409 = 90 + 473.53 = 563.53 \, \text{mg}C41​=90+C40​×0.8409=90+563.18×0.8409=90+473.53=563.53mg

C_42:

Za 42. nedelju:

C42=90+C41×0.8409=90+563.53×0.8409=90+473.89=563.89 mgC_{42} = 90 + C_{41} \times 0.8409 = 90 + 563.53 \times 0.8409 = 90 + 473.89 = 563.89 \, \text{mg}C42​=90+C41​×0.8409=90+563.53×0.8409=90+473.89=563.89mg

C_43:

Za 43. nedelju:

C43=90+C42×0.8409=90+563.89×0.8409=90+474.25=563.25 mgC_{43} = 90 + C_{42} \times 0.8409 = 90 + 563.89 \times 0.8409 = 90 + 474.25 = 563.25 \, \text{mg}C43​=90+C42​×0.8409=90+563.89×0.8409=90+474.25=563.25mg

C_44:

Za 44. nedelju:

C44=90+C43×0.8409=90+563.25×0.8409=90+474.61=563.61 mgC_{44} = 90 + C_{43} \times 0.8409 = 90 + 563.25 \times 0.8409 = 90 + 474.61 = 563.61 \, \text{mg}C44​=90+C43​×0.8409=90+563.25×0.8409=90+474.61=563.61mg

C_45:

Za 45. nedelju:

C45=90+C44×0.8409=90+563.61×0.8409=90+474.97=563.97 mgC_{45} = 90 + C_{44} \times 0.8409 = 90 + 563.61 \times 0.8409 = 90 + 474.97 = 563.97 \, \text{mg}C45​=90+C44​×0.8409=90+563.61×0.8409=90+474.97=563.97mg

C_46:

Za 46. nedelju:

C46=90+C45×0.8409=90+563.97×0.8409=90+475.34=564.34 mgC_{46} = 90 + C_{45} \times 0.8409 = 90 + 563.97 \times 0.8409 = 90 + 475.34 = 564.34 \, \text{mg}C46​=90+C45​×0.8409=90+563.97×0.8409=90+475.34=564.34mg

C_47:

Za 47. nedelju:

C47=90+C46×0.8409=90+564.34×0.8409=90+475.70=564.70 mgC_{47} = 90 + C_{46} \times 0.8409 = 90 + 564.34 \times 0.8409 = 90 + 475.70 = 564.70 \, \text{mg}C47​=90+C46​×0.8409=90+564.34×0.8409=90+475.70=564.70mg

C_48:

Za 48. nedelju:

C48=90+C47×0.8409=90+564.70×0.8409=90+476.06=564.06 mgC_{48} = 90 + C_{47} \times 0.8409 = 90 + 564.70 \times 0.8409 = 90 + 476.06 = 564.06 \, \text{mg}C48​=90+C47​×0.8409=90+564.70×0.8409=90+476.06=564.06mg

C_49:

Za 49. nedelju:

C49=90+C48×0.8409=90+564.06×0.8409=90+476.42=564.42 mgC_{49} = 90 + C_{48} \times 0.8409 = 90 + 564.06 \times 0.8409 = 90 + 476.42 = 564.42 \, \text{mg}C49​=90+C48​×0.8409=90+564.06×0.8409=90+476.42=564.42mg

C_50:

Za 50. nedelju:

C50=90+C49×0.8409=90+564.42×0.8409=90+476.78=564.78 mgC_{50} = 90 + C_{49} \times 0.8409 = 90 + 564.42 \times 0.8409 = 90 + 476.78 = 564.78 \, \text{mg}C50​=90+C49​×0.8409=90+564.42×0.8409=90+476.78=564.78mg

C_51:

Za 51. nedelju:

C51=90+C50×0.8409=90+564.78×0.8409=90+477.14=564.14 mgC_{51} = 90 + C_{50} \times 0.8409 = 90 + 564.78 \times 0.8409 = 90 + 477.14 = 564.14 \, \text{mg}C51​=90+C50​×0.8409=90+564.78×0.8409=90+477.14=564.14mg

C_52:

Za 52. nedelju:

C52=90+C51×0.8409=90+564.14×0.8409=90+477.49=564.49 mgC_{52} = 90 + C_{51} \times 0.8409 = 90 + 564.14 \times 0.8409 = 90 + 477.49 = 564.49 \, \text{mg}C52​=90+C51​×0.8409=90+564.14×0.8409=90+477.49=564.49mg

C_53:

Za 53. nedelju:

C53=90+C52×0.8409=90+564.49×0.8409=90+477.85=564.85 mgC_{53} = 90 + C_{52} \times 0.8409 = 90 + 564.49 \times 0.8409 = 90 + 477.85 = 564.85 \, \text{mg}C53​=90+C52​×0.8409=90+564.49×0.8409=90+477.85=564.85mg

C_54:

Za 54. nedelju:

C54=90+C53×0.8409=90+564.85×0.8409=90+478.21=564.21 mgC_{54} = 90 + C_{53} \times 0.8409 = 90 + 564.85 \times 0.8409 = 90 + 478.21 = 564.21 \, \text{mg}C54​=90+C53​×0.8409=90+564.85×0.8409=90+478.21=564.21mg

C_55:

Za 55. nedelju:

C55=90+C54×0.8409=90+564.21×0.8409=90+478.57=564.57 mgC_{55} = 90 + C_{54} \times 0.8409 = 90 + 564.21 \times 0.8409 = 90 + 478.57 = 564.57 \, \text{mg}C55​=90+C54​×0.8409=90+564.21×0.8409=90+478.57=564.57mg

C_56:

Za 56. nedelju:

C56=90+C55×0.8409=90+564.57×0.8409=90+478.92=564.92 mgC_{56} = 90 + C_{55} \times 0.8409 = 90 + 564.57 \times 0.8409 = 90 + 478.92 = 564.92 \, \text{mg}C56​=90+C55​×0.8409=90+564.57×0.8409=90+478.92=564.92mg

C_57:

Za 57. nedelju:

C57=90+C56×0.8409=90+564.92×0.8409=90+479.28=564.28 mgC_{57} = 90 + C_{56} \times 0.8409 = 90 + 564.92 \times 0.8409 = 90 + 479.28 = 564.28 \, \text{mg}C57​=90+C56​×0.8409=90+564.92×0.8409=90+479.28=564.28mg

C_58:

Za 58. nedelju:

C58=90+C57×0.8409=90+564.28×0.8409=90+479.63=564.63 mgC_{58} = 90 + C_{57} \times 0.8409 = 90 + 564.28 \times 0.8409 = 90 + 479.63 = 564.63 \, \text{mg}C58​=90+C57​×0.8409=90+564.28×0.8409=90+479.63=564.63mg

C_59:

Za 59. nedelju:

C59=90+C58×0.8409=90+564.63×0.8409=90+479.99=564.00 mgC_{59} = 90 + C_{58} \times 0.8409 = 90 + 564.63 \times 0.8409 = 90 + 479.99 = 564.00 \, \text{mg}C59​=90+C58​×0.8409=90+564.63×0.8409=90+479.99=564.00mg

C_60:

Za 60. nedelju:

C60=90+C59×0.8409=90+564.00×0.8409=90+480.35=564.35 mgC_{60} = 90 + C_{59} \times 0.8409 = 90 + 564.00 \times 0.8409 = 90 + 480.35 = 564.35 \, \text{mg}C60​=90+C59​×0.8409=90+564.00×0.8409=90+480.35=564.35mg

C_61:

Za 61. nedelju:

C61=90+C60×0.8409=90+564.35×0.8409=90+480.71=564.71 mgC_{61} = 90 + C_{60} \times 0.8409 = 90 + 564.35 \times 0.8409 = 90 + 480.71 = 564.71 \, \text{mg}C61​=90+C60​×0.8409=90+564.35×0.8409=90+480.71=564.71mg

C_62:

Za 62. nedelju:

C62=90+C61×0.8409=90+564.71×0.8409=90+481.06=564.06 mgC_{62} = 90 + C_{61} \times 0.8409 = 90 + 564.71 \times 0.8409 = 90 + 481.06 = 564.06 \, \text{mg}C62​=90+C61​×0.8409=90+564.71×0.8409=90+481.06=564.06mg

C_63:

Za 63. nedelju:

C63=90+C62×0.8409=90+564.06×0.8409=90+481.42=564.42 mgC_{63} = 90 + C_{62} \times 0.8409 = 90 + 564.06 \times 0.8409 = 90 + 481.42 = 564.42 \, \text{mg}C63​=90+C62​×0.8409=90+564.06×0.8409=90+481.42=564.42mg

C_64:

Za 64. nedelju:

C64=90+C63×0.8409=90+564.42×0.8409=90+481.78=564.78 mgC_{64} = 90 + C_{63} \times 0.8409 = 90 + 564.42 \times 0.8409 = 90 + 481.78 = 564.78 \, \text{mg}C64​=90+C63​×0.8409=90+564.42×0.8409=90+481.78=564.78mg

C_65:

Za 65. nedelju:

C65=90+C64×0.8409=90+564.78×0.8409=90+482.14=564.14 mgC_{65} = 90 + C_{64} \times 0.8409 = 90 + 564.78 \times 0.8409 = 90 + 482.14 = 564.14 \, \text{mg}C65​=90+C64​×0.8409=90+564.78×0.8409=90+482.14=564.14mg

C_66:

Za 66. nedelju:

C66=90+C65×0.8409=90+564.14×0.8409=90+482.49=564.49 mgC_{66} = 90 + C_{65} \times 0.8409 = 90 + 564.14 \times 0.8409 = 90 + 482.49 = 564.49 \, \text{mg}C66​=90+C65​×0.8409=90+564.14×0.8409=90+482.49=564.49mg

C_67:

Za 67. nedelju:

C67=90+C66×0.8409=90+564.49×0.8409=90+482.85=564.85 mgC_{67} = 90 + C_{66} \times 0.8409 = 90 + 564.49 \times 0.8409 = 90 + 482.85 = 564.85 \, \text{mg}C67​=90+C66​×0.8409=90+564.49×0.8409=90+482.85=564.85mg

C_68:

Za 68. nedelju:

C68=90+C67×0.8409=90+564.85×0.8409=90+483.21=564.21 mgC_{68} = 90 + C_{67} \times 0.8409 = 90 + 564.85 \times 0.8409 = 90 + 483.21 = 564.21 \, \text{mg}C68​=90+C67​×0.8409=90+564.85×0.8409=90+483.21=564.21mg

C_69:

Za 69. nedelju:

C69=90+C68×0.8409=90+564.21×0.8409=90+483.56=564.56 mgC_{69} = 90 + C_{68} \times 0.8409 = 90 + 564.21 \times 0.8409 = 90 + 483.56 = 564.56 \, \text{mg}C69​=90+C68​×0.8409=90+564.21×0.8409=90+483.56=564.56mg

C_70:

Za 70. nedelju:

C70=90+C69×0.8409=90+564.56×0.8409=90+483.92=564.92 mgC_{70} = 90 + C_{69} \times 0.8409 = 90 + 564.56 \times 0.8409 = 90 + 483.92 = 564.92 \, \text{mg}C70​=90+C69​×0.8409=90+564.56×0.8409=90+483.92=564.92mg

Zaključak:

  • Do 70. nedelje koncentracija leka u krvi se stabilizuje i osciluje oko 564.92 mg.
  • Sa svakim novim unosom doze leka (90 mg nedeljno), koncentracija neprestano raste, ali iznos smanjenja sa svakom nedeljom postaje sve manji zbog eksponencijalnog raspada leka.

Da li želite da analiziramo još nešto ili nastavimo sa detaljima?

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