Exponential Functions
Functions where the variable is the exponent.
Key idea
Functions where the variable is the exponent.
In depth
f(x) = a·bˣ with b > 0, b ≠ 1. The variable is in the exponent, so equal steps in x multiply the output by the same factor b. Growth happens if b > 1, decay if 0 < b < 1.
Worked example
f(x) = 3·2ˣ: f(0) = 3, f(1) = 6, f(2) = 12, f(3) = 24.
Formula
Real-world uses
- Modelling population growth, radioactive decay and the spread of a social media post
Common mistake
Confusing exponential x ↦ 2ˣ with power x ↦ x².
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 Exponential Functions?
Functions where the variable is the exponent. It is a topic at the advanced level in Algebra.
What is the formula for Exponential Functions?
The key formula is y = a·bˣ.
Where is Exponential Functions used in real life?
Real-world examples: Modelling population growth, radioactive decay and the spread of a social media post.
What should I learn before Exponential Functions?
Make sure you are comfortable with Complex Conjugates, the previous topic in Algebra.
What is a common mistake with Exponential Functions?
Confusing exponential x ↦ 2ˣ with power x ↦ x².
How can I practise Exponential Functions?
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 Exponential Functions?
Move on to Exponential Growth and Decay 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.