Exponential growth follows from the statement:

The population change between consecutives censuses is proportional to the population total of the current census.

Place 100 beads - varying amounts of white and black - 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.
• Return the bead to the cup.
• Record the population change.
• Compute the population total for the next census by adding the population change to the population total.