Exponential Growth and Decay
Constant percent change over equal time steps.
Key idea
Constant percent change over equal time steps.
In depth
Model quantities that change by a constant percentage over time: A = A₀(1 ± r)ᵗ. Population, radioactive decay, and compound interest all follow it.
Worked example
A population of 500 growing 4% per year: A = 500(1.04)ᵗ. After 10 years about 740.
Formula
Real-world uses
- Calculating medicine clearance from the body
- Depreciation of a car or inflation over years
Common mistake
Using 0.04 as the multiplier instead of 1.04.
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 Growth and Decay?
Constant percent change over equal time steps. It is a topic at the advanced level in Algebra.
What is the formula for Exponential Growth and Decay?
The key formula is A = A₀(1 ± r)ᵗ.
Where is Exponential Growth and Decay used in real life?
Real-world examples: Calculating medicine clearance from the body; Depreciation of a car or inflation over years.
What should I learn before Exponential Growth and Decay?
Make sure you are comfortable with Exponential Functions, the previous topic in Algebra.
What is a common mistake with Exponential Growth and Decay?
Using 0.04 as the multiplier instead of 1.04.
How can I practise Exponential Growth and Decay?
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 Growth and Decay?
Move on to The Number e 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.