# Math Insight

### Applet: Bacteria doubling

The evolution of this bacteria population follows a simple rule: the number of bacteria doubles every time step. Since the state of the system is determined by a single variable, the population size $b$, the state space is one-dimensional. The state space is represented by the blue vertical line at the left. The initial population size $b_0$ is a blue point and the population size $b_t$ at time $t$ is a red point on this state space. The time evolution of the dynamical system is also represented by the plot of population size $b_t$ versus $t$, where the lines connecting the points are not part of the graph but are there just to guide your eye. The population size $b_t$ is also illustrated in the right panel where each green dot represents one bacterium. You can change the time $t$ and the initial population size $b_0$ by moving the sliders in the gray box. Stop or start the animation by clicking the button that appears in the lower left corner of one of the panels.

Applet file: bacteria_doubling.ggb