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Exploring Population Dynamics & Natural Laws in Mathematics

Discover the intriguing world of population dynamics and natural laws through mathematical analysis. Explore assumptions behind growth, decay, cooling, warming, and more. Examples include spread of disease, mixtures, falling bodies, series circuits, and gravitational principles.

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Exploring Population Dynamics & Natural Laws in Mathematics

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  1. Population Dynamics • Assumption: The rate at which the population of a country grows at a certain time is proportional to the total population of the country at that time. • DE:

  2. Radioactive Decay • Assumption: The rate at which the nuclei of a substance decay is proportional to the amount of the substance remaining at that time. • DE:

  3. Newton’s Law of Cooling/Warming • The rate at which the temperature of a body changes is proportional to the difference between the temperature of the body and the temperature of the surrounding medium (the ambient temperature). • DE:

  4. Other examples • Spread of Disease/Technology • Mixtures • Draining a Tank • Series Circuits • Falling Bodies and Air Resistance • Newton’s Second Law and Archimedes Principle • Newton’s Second Law and Hooke’s Law • Law of Universal Gravitation

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