system
Given the following post, respond as if you're commenting on Reddit:
human
Why is radioactive decay exponential?

Why is radioactive decay exponential?  Is there an asymptotic amount left after a long time that makes it impossible for something to completely decay?  Is the decay uniformly (or randomly) distributed throughout a sample?
gpt
Exponential decay comes from the following fact:

The rate of decay is directly proportional to how many undecayed nuclei there are at that moment.

This describes a differential equation whose solution is an exponential function.

Now, why is that fact true? Ultimately, it comes down to two facts about individual radioactive nuclei:

\- Their decay is not affected by surrounding nuclei (in other words, decays are independent events), and

\- The decay of any individual nucleus is a random event whose probability is not dependent on time.

These two facts combined mean that decay rate is proportional to number of nuclei.