Keerthana M
2nd BSc (EMCs)
The constant was discovered by the swiss mathematician
Jacob Bernoulli while studying compound
interest . Later Euler started to use the letter ‘e’ for the constant in the
year 1727.
The number ‘e’ , is a mathematical constant, and it is
known as Euler’s number and the value of ‘e’ is approximately equal to 2.71828.
e
is not just a number it is most useful mathematical constant.
‘e’ is used in the base of the natural logarithm .
‘e’ is also used in the limits of 〖[1+1/n]〗^n
as n tends to infinity that arises in the study of
compound interest. It can also be calculated as the sum of the infinite series. Use of e is
in all branches of science and everyday life.
Euler's identity eiπ+1=0 helps for those dealing with complex analysis, such as computer
programming design for next revolutionary application, scientists planning for
mission to mars.
In physics it used to find behaviour of quantum particles and also
equations for light waves, sound waves
and quantum waves
'e' is used in probability theory. For
example consider the die of 4 sides is rolled 4 times and the chance of not rolling a 1 is 0.3164, The die of 6 sides is
rolled 6 times and the chance of not rolling a 1 is 0.3349, the die of
100 side is rolled 100 times and the chance of not rolling 1 is 0.366 , by this
we can say the
chance of rolling approximately equal to 1/e. That is 0.3679.
Take a pack of cards in proper order
Shuffle it if we do randomly then there is 1/e chance that no card is in its
original position.
e is used to calculate compound
interest, Invest
₹10,000 at 5%per annum for
7 years ,as we get interest frequently, the value
of investment for annual interest is ₹14,071, quarterly interest=₹14,160, monthly interest=₹14,180daily interest=₹14,190.
then by using exponentially it is 10,000 e^((.05*7)) =₹14,190.68.
Models for population growth and
decline: e is used to calculate population growth and decay by using formula
P=P0 ekt .
Where P= population growth after some
amount of time,
P0= initial population, k=
growth or decay rate, t= time.