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Exponential functions are mathematical functions that can describe extremely rapid growth or decay. Let's explore the properties of exponential functions through a real-world example.
Imagine the following scenario: Someone carries a virus and infects other people. Then, each of those people infects more people in the next phase.
If we track the number of infected people in each phase:
From the data above, a clear pattern emerges: the number of people infected in phase is .
If represents the number of people infected in phase , then:
This is an example of an exponential function.
Using the equations above, we can visualize the virus spread through the following graph:
Virus spread grows exponentially, accelerating rapidly after the initial phases.
How many people will be infected in phase ?
Which function best represents the virus spread?
Of the three graphs shown, the exponential graph most accurately depicts this virus spread. This graph shows slow growth initially but becomes very rapid as phases progress.
From the exploration above, we can conclude several properties of the exponential function (where and ):
Exponential functions are used in various fields:
Understanding exponential functions helps us analyze and predict phenomena that exhibit rapid growth or decay.
