Logistic growth follows from the statement:

The population change between consecutive censuses is proportional to both the current population total and to the difference between the population capacity and the current population total.

Place 50 white beads in a styrofoam cup. Put a lid on the cup with a small hole notched out of the edge to facilitate pouring 1 bead out of the cup. The white beads in the cup represent resources.

Here are the rules:

• At census 0, the population total is 1.
• Each member of the population looks for resources that will allow it to add one to the population.
• Pour out a bead for each member of the total population. If it is white, add one to the population change for the next census. If the bead is black, do not add to the population change.
• Replace the bead poured out of the cup with a black bead.
• Record the population change.
• Compute the population total for the next census by adding the population change to the population total.