What does exponential decay look like?
When amount of some substance is diminished by a constant factor every unit of time, we call this process an exponential decay.
Assume you have a mass
Measured in these units, after
We came up with a functional dependence of the remaining mass from the number of time units passed expressed by a general formula
This functional dependence is called exponential in mathematics, and that's why the process is called exponential decay.
The fact that the functional dependence is exponential is one reason for this name. The fact that the base of an exponential function is less than
Another interesting example is cooling off of a hot item, like a kettle after the water has reached the boiling point and we took it off the stove top.
The temperature is diminishing by a certain factor every unit of time, like by
If the initial temperature was
After the second minute the temperature above surrounding will be
which also represents an exponential dependency of the temperature