e is Everywhere

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 e^iπ+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 e^kt .

Where P= population growth after some amount of time,

P₀= initial population, k= growth or decay rate, t= time.