Explain eulers number
e \approx 2.718Transcript
Euler's number, written as e, is about two point seven one eight.
e \approx 2.718It shows up everywhere in nature, from bank interest to population growth.
Let's start with a bank account that doubles your money. But what if the bank compounds interest more often, like monthly or daily? Watch what happens as we compound more and more often.
- Start with 1 pound, it doubles each year
The answer gets closer and closer to e, about two point seven one eight. Here's the formula: e equals the limit of one plus one over n, all to the power n.
e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^nEuler's number is irrational, like pi, so its digits never end or repeat. Real example: if bacteria double every hour, starting with one cell, after t hours you have e to the power t cells.
- e = 2.71828182845904523...
- Exponential growth model
N(t) = e^tEuler's number e is the natural rate of growth that appears in exponential functions everywhere.
- e: nature's growth constant
