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

This applet is found in the pages

List of all applets

General information about Geogebra Web applets

This applet was created using Geogebra. In most Geogebra applets, you can move objects by dragging them with the mouse. In some, you can enter values with the keyboard. To reset the applet to its original view, click the icon in the upper right hand corner.

You can download the applet onto your own computer so you can use it outside this web page or even modify it to improve it. You simply need to download the above applet file and download the Geogebra program onto your own computer.