Technical Math: Exponential Equations & Functions

 

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Relevant Material: "Exponential equations and functions are used in real-life to model phenomena with rapid growth or decay, such as population growth, compound interest, radioactive decay, and the amount of medicine in the bloodstream. They help in making predictions about future events by showing how things change over time, or in other scenarios like predicting the temperature of an object cooling down, as explained by Mathematics LibreTexts. 
Key applications:
  • Finance: Exponential functions are used to calculate compound interest on savings, loans, and investments, showing how money grows over time.
  • Population Dynamics: They model the growth of populations (animal and human) and are used to predict future population sizes.
  • Science and Medicine:
    • Radioactive Decay: The decay of radioactive materials is modeled exponentially, which is crucial for applications like carbon-14 dating.
    • Medicine: They can determine the amount of a drug remaining in the body over time, or the time it takes for a drug's concentration to reach a certain level.
    • Cooling: Newton's Law of Cooling uses exponential functions to predict how an object's temperature changes as it cools or warms to match its environment.
  • Other fields:
    • Fluid Dynamics: Predicting fluid flow rates.
    • Forensics: Analyzing evidence, such as the rate at which a body cools, can help estimate the time of death.
    • Computer Science: Zooming in on a screen a certain number of times can be modeled exponentially, as shown in this Reddit thread.
    • Seismology: The Richter scale uses an exponential scale to measure earthquake intensity. .." (Google) 
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