MathBench > Visualization

Log Transformations

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.

Can you predict what the transformed graph will look like BEFORE you place the points?

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So, both the left side of the graph is a straight line heading up -- because the bacteria are growing exponentially, i.e., multiplying by a constant fact. And the right side of the graph is a straight line heading down -- because the bacteria are dying off exponentially, i.e., each timestep there is a constant fraction of the number there were the timestep before. These straight lines are diagnostic of exponential growth and exponential decay.