Calculus › Section G · Differential equations › Topic G.2
Exponential growth and decay
The simplest differential equation of all, rate proportional to current value, governs bacteria, radioactivity and bank balances alike. Its solution is one line long, and the same few formulas answer questions in biology, physics and finance.
In this topic
- The simplest model of all
- The solution, one line
- Growth versus decay
- Doubling time and half-life
- Worked example: a bacterial colony
- Worked example: carbon dating
- Interest as a growth process
- Modelling honesty
- Common mistakes to avoid
- Key takeaways
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Standards: 7