Tech Math: Geometric Series

 

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Relevant Material: "Geometric sequences and series are used in applications involving exponential growth and decay, such as calculating compound interest and radioactive decay, modeling population growth, and analyzing drug absorption or elimination in pharmacology. They are also applied in fields like mechanical engineering for gear systems and finance for situations like salary increases or depreciation. 
Finance
  • Compound interest: Calculates how investments grow exponentially over time, as the interest earned is added to the principal, and the next interest calculation is based on the new, larger amount.
  • Depreciation: Models the decrease in an asset's value over time by a fixed percentage each year.
  • Salary growth: Can be used to model a salary that increases by a fixed percentage each year. 
Science and Nature
  • Population growth: Models the growth of a population that increases by a constant factor over time.
  • Bacterial growth: Tracks the exponential increase of a bacterial colony.
  • Radioactive decay: Determines the remaining amount of a radioactive substance over time, where the amount decreases by a fixed percentage (the half-life) in each period. 
Other Applications
  • Pharmacology: Models the absorption, distribution, metabolism, and excretion of a drug in the body, which can follow a geometric progression over time.
  • Mechanical engineering: Used in the design of gear systems where the ratio of teeth between gears can follow a geometric sequence.
  • Fractals: Used to model the infinite perimeter and finite area of shapes like the Koch snowflake.
  • Real-world scenarios: Can compare payment plans, such as a fixed daily increase versus a daily doubling of pay, to see which results in a larger total earning over time, notes a YouTube video. .." (google) 
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