The Number e
The base where growth rate equals value.
Key idea
The base where growth rate equals value.
In depth
e ≈ 2.71828 is the limit of (1 + 1/n)ⁿ as n grows. It is the base for which the rate of growth equals the current value, making eˣ its own derivative. It describes continuous growth.
Worked example
Continuous compounding: 1000 at 5% for 2 years = 1000e^(0.1) ≈ 1105.17.
Formula
Real-world uses
- Continuous interest in finance
- Natural growth models in biology and physics
Common mistake
Treating e as a variable. It is a fixed constant.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is The Number e?
The base where growth rate equals value. It is a topic at the advanced level in Algebra.
What is the formula for The Number e?
The key formula is e = lim (1+1/n)ⁿ ≈ 2.71828.
Where is The Number e used in real life?
Real-world examples: Continuous interest in finance; Natural growth models in biology and physics.
What should I learn before The Number e?
Make sure you are comfortable with Exponential Growth and Decay, the previous topic in Algebra.
What is a common mistake with The Number e?
Treating e as a variable. It is a fixed constant.
How can I practise The Number e?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after The Number e?
Move on to Logarithms next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.