Why is radioactive half-life important?

I can think of three reasons why half-life is important.
A knowledge of radioactive half-life is important because

It enables the dating of artifacts.

It allows us to calculate how long we must store radioactive waste until they become safe.

It enables doctors to use safe radioactive tracers.

Half-life is the time it takes for one-half of the atoms of a radioactive material to disintegrate.
Scientists can use the half-life of carbon-14 to determine the approximate age of organic objects. They determine how much of the carbon-14 has transformed. They can then calculate the age of a substance.
All nuclear reactors produce radioactive waste. The waste must be stored until it is safe for disposal.
The rule is that a sample is safe after 10 half-lives. Thus, we can dispose of waste containing iodine-131 (##t_½## = 8 days) after 80 days.
We must store the plutonium-239 in spent nuclear fuel (##t_½## = 24 000 years) for almost a quarter of a million years.
Doctors use radioactive as medical tracers.
The nuclei must be active long enough to treat the condition, but they must also have a short enough half-life so that they don’t have time to injure healthy cells and organs.