Answer:
Step-by-step explanation:
Geometric progressions happen whenever each agent of a system acts independently. For example population growth each couple do not decide to have another kid based on current population. So population growth each year is geometric. Each radioactive atom independently disintegrates, which means it will have fixed decay rate. In other words that is why there is "half-life" of a radioactive element, in a fixed amount of time it becomes half. Email chains, Interest rate, etc are more examples of the same kind.
On the other end global/singular decisions give arithmetic progressions. If you add a fixed amount to your piggy bank each week that is arithmetic progression. 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. There are exceptions of course like the ball bouncing is geometric even though it is singular because of coefficient of restitution. In general singular decisions can be anything - but typically arithmetic.
In reality, these are ideal cases, most of the natural phenomenon will have both global and local influencers. Making it somewhere in between arithmetic and geometric progressions.
If the population is already huge having another kid might not be so conducive. So the population growth will stop when overall resources get limited. 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.
Tumour growth, the growth rate is exponential unless it becomes so large that it cannot get food to grow effectively. So it starts of exponentially and stops completely. A more precise statement is known as Gompertz Law of Mortality - "rate of decay falls exponentially with current size".
