First introduction
When we studied the logarithm function it was introduced to us a transcendental number kown with the letter e. e has a value of approximately 2.71828 and it was discovered by Jacob Bernoulli in 1683. The difficulty of this constant is that it is not defined in geometry (like π) but we need a different approach to define it. This constant is related to the rate of change and growth and we are going to deduce why.
A simple experiment to introduce what e actually is
Let me introduce you to a simple but functional example which is correlated to the study of Bernoulli: imagine going to a generous bank and deposit 1$, the bank tells you that next year you will be earning 100% more of what you have previously deposited. So how much $ would you have? 2$! Now let's imagine you go to another bank (more generous than the other one) and in this bank the interest rate it's 50% every 6 months; how much money would you have? 1+50% of 1 in the first 6 months which is 1.50 than 1.50+50% of 1.50 which is 2.25. Wow! we earned more money than the previous bank. Let's try this one more time and see what happens; so we are going to have +25% every 3 months. The result would be approximately 2.4414. If we continue this process again and again with smaller and smaller time (a month, a week, a day, a second and so on) and interest rate we notice that we are approaching the famous constant e.
Some applications of e
This letter has an important role in mathematics for example in calculus. One curiosity for people who are reading this article that haven't already studied derivatives is that the derivative of e to the x is actually e to the x, and the derivative of the other exponentials functions are strongly related to e. Another important usage of the letter e is found on the Euler's formula(Euler is actually the first one who give the constant e his letter and name) which is considered one of the most beautiful math's identity because it relates 5 of the most important numbers: e, π, i, 1 and 0.
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