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Exponential growth and decay models real situations — populations, radioactive decay, cooling and compound interest — using functions of the form A = A₀eᵏᵗ. It covers forming and interpreting models, finding rates and using logarithms to solve for time or the growth constant. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Fit a model of the form A times e to the kt, using the initial condition to find A and a second data point to find k. A positive k means growth and a negative k decay. Take logs to solve for t.
Before you start
Best tackled after natural logarithms and exponentials. It is Pure 3 content. Keep it sharp for differential equations and modelling.
What you learn
The course works through solving for the time, bounded models and the limiting value, rational / logistic models and rates of change. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Exponential Growth & Decay is a Exponentials & Logarithms topic in the A-level syllabus, covered here at the second year of A-level. You work through 6 concepts and 6 worked examples, testing yourself at 6 points. Nearby topics in the same strand are Introducing Logarithms, Laws of Logarithms, Logarithmic Graphs (Linear Form), Natural Logarithms & e and Solving Equations Using Logarithms. You can drill this strand further on the Exponentials & Logarithms revision engine, with your accuracy saved to your skill tree.
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