why natural phenomena follow exponential growth?

Hi


1: In the context of the definition given below, what does the word "shallower" mean? Here is given the **broken link removed**.

exponential
Something is said to increase or decrease exponentially if its rate of change must be expressed using exponents. A graph of such a rate would appear not as a straight line, but as a curve that continually becomes steeper or shallower.

The American Heritage Science Dictionary

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2: I have read that many phenomena in nature follow exponential growth. Why is so? Could you please explain how this connection is established between nature and mathematical world? Obviously, if bacterial follows exponential growth, then it is not under any obligation to do so, it does it unknowingly. Besides exponential growth, what other type of growth the natural phenomena most often follow? Please don't use more math to explain math. Thank you.

Regards
PG

Hi

PG1995 said:

1: In the context of the definition given below, what does the word "shallower" mean? Here is given the **broken link removed**.

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[LATEX]y=e^{-x}[/LATEX] as opposed to [LATEX]y=e^x[/LATEX] ?

what does the word "shallower" mean?

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It means 'less steep', like a hill which is steep at the base but flattens out towards the top.

Besides exponential growth, what other type of growth the natural phenomena most often follow?

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Consider a plant increasing in height at a steady rate of 1cm per week. That is a linear growth rate, with a constant rate of change.

many phenomena in nature follow exponential growth. Why is so?

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Consider bacterial replication. Let's suppose it takes 1 second for a bacterium to grow and then divide into two. After 1 sec there will be 2 bacteria. They will also grow and divide, so after 2 secs there will be 4 bacteria. And so on. So the bacterium population, as each second passes, will be 1,2,4,8,16,32,......... which is an exponential population growth rate. This is characterised by a rate of change which is not constant, but instead increases in proportion to the existing population size.