WHEN THE NUMBERS EXPLODE!

 

    "The greatest shortcoming of the human race is our inability to understand the exponential function". said a great physicist.
     This can be illustrated by a simple story.  Once a king a offered a reward to a poet.  He asked the poet what he desired to have?  The poet replied,"chess board filled up with grains".  The king exclaimed,"what"?.  The poet said, "I want a chess board filled up with grains in this way.  Put one grain on first square, two on second square, four on third square.  Every time double the number of grains and fill up all the 64 squares".  Anyway, the king ordered the servants to carry out the poet's wish.
     Half way through the process the numbers exploded.  The king realized the reward could not be fulfilled even if he used all the grains in the kingdom. That is the power of exponential function.  Here the function is 

Y =2^x,   2^0=1, 2^1=2,  2^2=4,  2^3=8.......2^64= 1.8 followed by 19 zeros

     Moore's law is the consequence of this principle.  It says,"Number of transistors in a silicon chip doubles every 18 months".  That is why we spent 25 years with Bulky desk-top and then rapidly switched over to smart phones.
     The spread of viruses often works in a similar way.  One ill person infects a few others, who in turn each infect a few more, until it becomes an epidemic.  Immunization is necessary to control the break out.
     If you want to save for retirement, start early.  Even a little delay will cost you so much.  If you save 250 dollars every month from age 18,  you will get more than a million dollars at 65.  But, if you start the savings at 30, you will only reach 478 thousand dollars at 65.  Here compound interest comes into play.
     If we fail to understand exponential growth, our debts can rapidly spiral out of control too.  Exponential function is both the creator and destroyer. Chain reaction in Nuclear bomb, Laser action in a laser device, snow balling, avalanche, growth of bacterial population....all examples of exponential explosion.

FOOT NOTE: 
Y =e^x
    Where e=2.71... Euler number.  It is a special function used for natural growth and decay.  You can say 'e' is the unit of growth or decay.  "If one unit grows continuously or exponentially for unit time, it will grow from 1 to maximum 2.71... units,  that is e.
    Hence numbers do explode.
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