System decay over time

Published: 18 December 2023| Version 1 | DOI: 10.17632/3mwt9s3vkr.1
Sunil Maria Benedict


If we consider a graph representing the learning outcomes or progress over time, it might align with the concept of impermanence or change in educational contexts. The graph could showcase the evolution of student learning or mastery of course material over the duration of a term or course. Initially, at the start (t=0), students might have varying levels of understanding or competence, represented by different points on the graph. As learning progresses over time, the graph would ideally depict an upward trend, indicating improvement or growth in knowledge and skills. However, this growth might not always be linear; there could be fluctuations or variations in the learning curve, symbolizing the transient nature of learning. The graph might exhibit periods of rapid improvement (steeper slopes) where new concepts are introduced or understood quickly, followed by plateaus or slower growth phases. These plateaus or fluctuations can represent the moments when understanding stabilizes or when the learning process temporarily slows down. At the end of the term or course, the graph might show a higher average level of learning or competency compared to the beginning. However, the key concept of impermanence comes into play here: once the course concludes, the learning curve might start to decline or level off if the knowledge isn't consistently reinforced or applied.


Steps to reproduce

import numpy as np import matplotlib.pyplot as plt # Constants k = 0.1 # Decay constant # Initial condition N0 = 100 # Initial quantity or state of the system # Time values t = np.linspace(0, 50, 100) # Time from 0 to 50 with 100 steps # Solve the differential equation for exponential decay N = N0 * np.exp(-k * t) # Plotting plt.figure(figsize=(8, 6)) plt.plot(t, N, label='System State N(t)', color='blue') plt.title('System Decay Over Time') plt.xlabel('Time') plt.ylabel('System State') plt.legend() plt.grid(True)


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