Here is one last dataset. This data represents the biomass of bacteria growing in a medium. At first there are virtually unlimited resources, and the bacteria multiply at a constant rate. Later, when the bacteria reach the limit of the resources, there is a period of steady population size. Finally the population declines as resources are exhausted.
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Popn. size | 0.1 | 1.8 | 32.4 | 583 | 500 | 600 | 35 | 2 | 0.12 |
Can you predict what the transformed graph will look like BEFORE you place the points?
The left side of the graph is a straight line heading up — because the bacteria are growing exponentially, i.e., multiplying by a constant factor. The right side of the graph is a straight line heading down — because the bacteria are dying off exponentially, i.e., at each time step there is a constant fraction of the number there were at the previous time step. These straight lines are diagnostic of exponential growth and exponential decay.