Looking for a good example of a naturally occuring compounding process

[musicgold]

TL;DR Summary

Looking for a natural process that can be used to explain the idea of compounding to an 8 year old. I want to highlight her the cummulative effet of small but regular increments.

She is not ready yet to understand the commonly-used example in the field of finance. I don't want to use the growth of a tree's trunk because the process is too slow.

I have also told her the 'chess board and rice grain story', but in that story the growth rate is very fast, so doesn't have the effect (small but regular increments) I want to show.

Also, it would great if you could suggest a game or simulation that could be useful in this case.

Thanks

 

[Office_Shredder]

Hmmm.

Population growth of humans isn't really purely exponential but not a terrible example if it makes sense.

Moore's law of computing power might be intuitive - 20 years ago computers couldn't even run the first ten frames of a modern video game etc.

 

[berkeman]

Summary:: Looking for a natural process that can be used to explain the idea of compounding to an 8 year old. I want to highlight her the cummulative effet of small but regular increments.

Also, it would great if you could suggest a game or simulation that could be useful in this case.

Maybe check out the Game of Life, where you can tune the different things that affect a population. If you turn the predator influence down, you get exponential quadratic growth...

(see the correction by @mfb below)

https://en.wikipedia.org/wiki/Conway's_Game_of_Life

 

[sysprog]

I think that a simple and perspicuous illustration would be the growth of a snowball during the making of a snowman.

 

[mfb]

Population growth in general, doesn't have to be limited to humans.

Not strictly exponential, but how fire can grow might be interesting as well. Can be combined with a fire safety lesson.

Maybe check out the Game of Life, where you can tune the different things that affect a population. If you turn the predator influence down, you get exponential growth...

https://en.wikipedia.org/wiki/Conway's_Game_of_Life

Elements can't propagate faster than linear in time, so at most you get quadratic growth. There are quadratic growth patterns with the regular rules, too. The second image has an example, a moving pattern that leaves glider guns behind.

 

[Mark44]

Another good example is the spread of infectious diseases, at least in the beginning of the cycle, while there are still uninfected members of the population.

 

[cgrie]

mosquitos?

 

[Stephen Tashi]

Cutting up a fruit by cutting it in half and then cutting each half in halves etc. ?

Of course, the focus in that case is on the increase in the total number of pieces, not the total mass of the pieces. So it doesn't convey the idea of increase in mass which is present in situations like the growth of animal populations.

An arrangement of dominoes where each domino knocks over several others?

 

[Klystron]

How about human growth patterns?

Children eating a proper diet exercise and grow over time. Or an athlete develops certain muscle groups that grow with use or shrink with inactivity. Unsure this meets the mathematical criteria but does contain healthy life lessons for an eight year old.