![]() ![]() Tumour growth, the growth rate is exponential unless it becomes so large that it cannot get food to grow effectively. Thomas Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources. So the population growth will stop when overall resources get limited. If the population is already huge having another kid might not be so conducive. Making it somewhere in between arithmetic and geometric progressions. In reality, these are ideal cases, most of the natural phenomenon will have both global and local influencers. In general singular decisions can be anything - but typically arithmetic. There are exceptions of course like the ball bouncing is geometric even though it is singular because of coefficient of restitution. The child who swings extra each time is likely to give only a constant extra force each time, so it is not likely for that to be geometric, it will be an arithmetic progression. ![]() If you add a fixed amount to your piggy bank each week that is arithmetic progression. On the other end global/singular decisions give arithmetic progressions. Email chains, Interest rate, etc are more examples of the same kind. In other words that is why there is "half-life" of a radioactive element, in a fixed amount of time it becomes half. Each radioactive atom independently disintegrates, which means it will have fixed decay rate. So population growth each year is geometric. For example population growth each couple do not decide to have another kid based on current population. Geometric progressions happen whenever each agent of a system acts independently. Using the examples other people have given. I like to explain why arithmetic and geometric progressions are so ubiquitous. ![]()
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