**This task is on the NRICH website and is the beginning of a fairly advanced collection of explorations into population dynamics. It is probably best undertaken in groups, so that each stage can be thoroughly discussed. **

**The beginning tasks are not inherently difficult mathematically, involving algebraic expressions of understandable situations. Exponential growth appears soon, and here the algebraic expression gets more unfamiliar, but the underlying sense of exponential growth should be familiar to learners from contexts outside school or in science. **

**This set of tasks is an introduction to the modelling process in a real context, so that students can appreciate the power of mathematics to provide a window on phenomena and predictive tools.**