ChatGPT Revenue Growth Prediction Using Logistic Model with Time Delay and Runge-Kutta Method.
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| Title: | ChatGPT Revenue Growth Prediction Using Logistic Model with Time Delay and Runge-Kutta Method. |
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| Authors: | Purwani, Sri1 sri.purwani@unpad.ac.id, Oktaviansyah, Eka2 eka17002@mail.unpad.ac.id, Harahap, Hisar Asman Mirsa2 hisar24001@mail.unpad.ac.id, Susanti, Dwi1 dwi.susanti@unpad.ac.id |
| Source: | Engineering Letters. Jul2026, Vol. 34 Issue 7, p2609-2616. 8p. |
| Subjects: | ChatGPT, Logistic functions (Mathematics), Computer simulation, Business forecasting, Runge-Kutta formulas, Business planning, Error analysis in mathematics |
| Abstract: | Logistic growth models are a common approach in modelling systems with a carrying capacity. In many real cases, however, there is a time delay between cause and effect in growth dynamics, such as in the case of revenue being affected by previous activities. This study applies a logistic model with time delay to simulate the revenue growth of ChatGPT and compares it with actual data. The Runge-Kutta method of order 4 (RK4) is used to solve the model numerically with a specific approach to the delay value. The simulation results show that the model is able to represent the transition from the fast growth phase to the saturation phase. ChatGPT revenue is predicted to reach a maximum of $4.026e+8 in the 36th month, and then enter a steady state. Evaluation of the model performance is done through error calculation, with a Mean Absolute Percentage Error (MAPE) value of 30.46% and a Root Mean Squared Error (RMSE) of 7,884,600.48. These results show that the model has a fairly good level of fit to the actual data and can represent the growth trend of ChatGPT revenue. This research confirms that a logistic model with time delay is an effective approach in modelling dynamic systems with historical influences, and can be used as a basis for strategic planning and decision-making in AI-based businesses. [ABSTRACT FROM AUTHOR] |
| Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: ChatGPT Revenue Growth Prediction Using Logistic Model with Time Delay and Runge-Kutta Method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Purwani%2C+Sri%22">Purwani, Sri</searchLink><relatesTo>1</relatesTo><i> sri.purwani@unpad.ac.id</i><br /><searchLink fieldCode="AR" term="%22Oktaviansyah%2C+Eka%22">Oktaviansyah, Eka</searchLink><relatesTo>2</relatesTo><i> eka17002@mail.unpad.ac.id</i><br /><searchLink fieldCode="AR" term="%22Harahap%2C+Hisar+Asman+Mirsa%22">Harahap, Hisar Asman Mirsa</searchLink><relatesTo>2</relatesTo><i> hisar24001@mail.unpad.ac.id</i><br /><searchLink fieldCode="AR" term="%22Susanti%2C+Dwi%22">Susanti, Dwi</searchLink><relatesTo>1</relatesTo><i> dwi.susanti@unpad.ac.id</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Engineering+Letters%22">Engineering Letters</searchLink>. Jul2026, Vol. 34 Issue 7, p2609-2616. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22ChatGPT%22">ChatGPT</searchLink><br /><searchLink fieldCode="DE" term="%22Logistic+functions+%28Mathematics%29%22">Logistic functions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Business+forecasting%22">Business forecasting</searchLink><br /><searchLink fieldCode="DE" term="%22Runge-Kutta+formulas%22">Runge-Kutta formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Business+planning%22">Business planning</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Logistic growth models are a common approach in modelling systems with a carrying capacity. In many real cases, however, there is a time delay between cause and effect in growth dynamics, such as in the case of revenue being affected by previous activities. This study applies a logistic model with time delay to simulate the revenue growth of ChatGPT and compares it with actual data. The Runge-Kutta method of order 4 (RK4) is used to solve the model numerically with a specific approach to the delay value. The simulation results show that the model is able to represent the transition from the fast growth phase to the saturation phase. ChatGPT revenue is predicted to reach a maximum of $4.026e+8 in the 36th month, and then enter a steady state. Evaluation of the model performance is done through error calculation, with a Mean Absolute Percentage Error (MAPE) value of 30.46% and a Root Mean Squared Error (RMSE) of 7,884,600.48. These results show that the model has a fairly good level of fit to the actual data and can represent the growth trend of ChatGPT revenue. This research confirms that a logistic model with time delay is an effective approach in modelling dynamic systems with historical influences, and can be used as a basis for strategic planning and decision-making in AI-based businesses. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 2609 Subjects: – SubjectFull: ChatGPT Type: general – SubjectFull: Logistic functions (Mathematics) Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Business forecasting Type: general – SubjectFull: Runge-Kutta formulas Type: general – SubjectFull: Business planning Type: general – SubjectFull: Error analysis in mathematics Type: general Titles: – TitleFull: ChatGPT Revenue Growth Prediction Using Logistic Model with Time Delay and Runge-Kutta Method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Purwani, Sri – PersonEntity: Name: NameFull: Oktaviansyah, Eka – PersonEntity: Name: NameFull: Harahap, Hisar Asman Mirsa – PersonEntity: Name: NameFull: Susanti, Dwi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1816093X Numbering: – Type: volume Value: 34 – Type: issue Value: 7 Titles: – TitleFull: Engineering Letters Type: main |
| ResultId | 1 |
