## 1 Introduction  
Quantifying athletic performance through mathematical models has been a cornerstone in exercise physiology for decades, as these models provide objective insights into the physiological processes behind athletic output [1]. Among these, the Critical Power Model (CPM) is a widely adopted approach, serving as a benchmark across sports to delineate an athlete's aerobic and anaerobic energy contributions during exercise [2]. This model breaks down performance into two components: critical power (CP), the maximum sustainable power through aerobic means, and work capacity (W\({}^{\prime}\)), the finite anaerobic reserve tapped into for short, intense efforts. CP and W\({}^{\prime}\) provide a powerful framework for tailoring training interventions to an athlete's unique needs and have become valuable tools in various applications, including monitoring training load and guiding pacing strategies [3; 4; 5]. Traditional CP and W\({}^{\prime}\) assessments involve exhaustive, multi-day testing, requiring athletes to complete several high-intensity trials spaced out over several days to avoid fatigue effects. This method captures a range of intensities, from short sprints to sustained efforts, forming the power-duration relationship from which CP and W\({}^{\prime}\) can be derived. While accurate, this protocol is time-intensive, physically demanding, and logistically challenging, often requiring up to a week to complete. For athletes and coaches, this makes frequent monitoring impractical, limiting the utility of these metrics in ongoing training and competition contexts [6]. In light of these challenges, alternative methods, such as single-session tests, have emerged. The 3 min all-out test (3 MT), proposed by [PERSON] (2006) [PERSON] (2006), exemplifies this by condensing the assessment into a single maximal effort session. During the 3 MT, athletes sustain maximum effort for three minutes, reaching a steady-state power output near the end (end power, or EP), which closely approximates CP. This approach captures the aerobic threshold without the need for multiple tests, while the total work above EP correlates with W\({}^{\prime}\), offering a more practical yet reliable means of estimating both CP and W\({}^{\prime}\)[PERSON] (2006). Validation studies have shown that 3 MT-derived estimates of CP and W\({}^{\prime}\) are comparable to those from traditional testing protocols with minimal statistical differences, supporting the utility of the 3 MT for both aerobic and anaerobic assessments [PERSON] (2006). However, the high intensity of the 3 MT remains a barrier for some athletes, as sustaining maximum effort for three minutes is both mentally and physically taxing. Research has shown that shorter test durations may yield similar accuracy in CPM parameters while being more acceptable to athletes. For instance, pacing strategies and test modifications, such as reduced test durations, have been suggested to improve feasibility without compromising accuracy ([PERSON], 2014; [PERSON], 2014). Shorter all-out efforts may reduce perceived exertion and make the 3 MT more adaptable for frequent monitoring, potentially broadening its application in performance assessments and training adaptations ([PERSON], 2014; [PERSON], 2014). Alternative mathematical models have frequently been applied to the traditional Critical Power Model ([PERSON], 2006), providing further insight into optimizing testing protocols. An examination of the 3 MT reveals a consistent trend of a fast, steep initial decrease in power output, followed by a gradual leveling off to an asymptotic power intensity. This characteristic power output pattern is similarly reflected in exponential-decay functions (mono- and bi-exponential), which may be leveraged to estimate an asymptote using a shorter duration dataset. Therefore, the purpose of this study was to assess the ability of exponential functions to further reduce the duration of the 3 MT while maintaining its accuracy in estimating CPM parameters.