The Number e
e ≈ 2.718 is the natural base of continuous growth.
About this topic
The number e ≈ 2.71828 is an irrational constant that appears when growth is compounded continuously. It is the limit of (1 + 1/n)ⁿ as n becomes infinite. The formula A = Pe^(rt) models continuous compounding and natural growth.
You can see the idea by trying larger n: with n = 1 you get 2, n = 10 gives 2.594, n = 1000 gives 2.717, and the values settle toward 2.71828. Imagine 1 dollar at 100% interest: compounding more and more often never gives more than e dollars at the end of the year. Continuous compounding of 1000 dollars at 5% for 10 years gives 1000e^0.5, about 1648.72.
e is special because the function eˣ is its own derivative, so its slope at every point equals its height, which makes it central to calculus. It appears in population growth, radioactive decay, the normal distribution in statistics, and the cooling of objects. Like pi, e never ends or repeats.
Do not confuse e with a variable or with the exponent symbol on a calculator. It is a fixed number, and the button usually looks like eˣ.
Key ideas
- e = lim (1 + 1/n)ⁿ
- eˣ is its own derivative
- Appears in continuous compounding
Quick check
Use cases: where The Number e helps
- Homework: review the key idea behind The Number e before you start a problem set.
- Exam revision: use the quick check to test whether you can recall The Number e without notes.
- Visual learning: play with the interactive lab to see how The Number e changes when you adjust its inputs.
- Teaching a friend: explain The Number e in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is The Number e?
e ≈ 2.718 is the natural base of continuous growth.
What will I learn in The Number e?
e = lim (1 + 1/n)ⁿ. eˣ is its own derivative. Appears in continuous compounding.
Is The Number e part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the The Number e lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study The Number e?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.