What are some situations where growth occurs arithmetically and what are situations where growth occurs exponentially?

In arithmetic progression  every next term increases with a fixed quantity:A.P  is  with  first tem a and a common difference d is:  a, a+d, a+2d, a+3d, a+4d, etc

The exponentioal growth is also geometric progression, where every next term increases or decreases by a fixed ratio: The exponential initial population a and growth factor x is of the type:

a, a(1+x) , a(1+x)^2, a(1+x)^3, a(1+x)^4, etc

The exponential growth of a population a, with a fixed ratio or factor could be like: a,   ax,   ax^2,  ax^3,   ax^4, etc,

Situations: In practical situations the amount of growth of $100 by a simple interest of 5% annually . The amount you are likely to get along with interest if you invest for 1 year , 2 year, 3 year , 4 year etc is: $105,   $110,  $115,  $120, etc...

If you invest an amount of $100 in compound interest of 5% (annual compounding) ,for  a period of an year , 2years, 3years, 4 years etc, your amount grows exponentially like.

100*1.05,   100*1.05^2,  100*1.05^3, 100*1.05^4,  ...etc.

Also you can see that  human population grows  exponentially, but with several constraints like food and space of the planet.There are similar exponential growth in living organisms in Biolological situations, where the species  increase exponentially and then decrease exponentially due nature's control.

Example: There are 10000 number of paticular species. If the growth rate is 10 % every 6 months how long it take for the population to double:

10000(1+10/100)^n =2*10000, whre n is the number of 6 months required for the population to double. Solution is   n = (log2/log1.1 ) of 6 months.