Euler’s number and its significance in real life.
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Not really a direct real-world application, but it is very useful in applications of maths:
e^x is its own derivative. As a result, it provides a convenient basis for many applications of exponential growth, where instead of a^x you can write e^(bx) where the growth rate is then equal to b*e^(bx), i.e. b times the amount you have at that moment.
Furthermore, because e^x is its own derivative it is a common solution to differential equations, which are the type equations that most physical models are based on
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