Suppose you are culturing a particular bacteria that reproduces by binary fission. Preliminary studies indicate that the population doubles every three hours under optimal laboratory conditions. As shown in this animation the number of bacteria grows exponentially with each successive generation.

Given this information, how would you answer the following questions?

1. How many bacteria will be present after 51 hours if you inoculate a culture with 1 bacterium?
2. How many bacteria should you inoculate a culture with if there are to be 81,920 bacteria present on hour 42?

You may be able to inefficiently answer these questions by brute force or trial and error. Luckily, a quick and easy method of solution is available when you know about exponential functions.

 

Exponential functions in biology

In fact, exponential functions are used in a variety of applications in the biological sciences including (but not limited to): population growth, pH, radioactive decay, and heat loss.

We will return to a discussion of the above questions in the Applications section where complete solutions will be provided.

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In the next section we will introduce a formal definition of an exponential function and provide some examples.