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.
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.