# What does exponential decay look like?

##### 1 Answer

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

After

After

etc.

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 *decay*, which means "diminishing".

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

etc.

After

which also represents an *exponential* dependency of the temperature