ChatGPT Revenue Growth Prediction Using Logistic Model with Time Delay and Runge-Kutta Method.

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Bibliographic Details
Title:	ChatGPT Revenue Growth Prediction Using Logistic Model with Time Delay and Runge-Kutta Method.
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]
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Database:	Engineering Source

Description
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]
ISSN:	1816093X