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There are many situations the rate of change in the quantity of something (over a fixed period of time) is proportional to the amount at the start of the period. Some typical examples are:

  • radioactive decay (physics)
  • depreciation (economics/accounting)
  • [uncontrolled] population growth (Biology, especially microbiology).
  • compound interest (banking)
The values form geometric progressions, so a study of the topic permits a better understanding of the development of the quantity over time.
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Q: Importance of geometric progression
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