8: Just add realism

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?

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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.