All organic material has decaying Carbon-14 in it. However, plants and animals that are still alive constantly replace the supply of carbon in their systems, so the amount of Carbon-14 in the system stays nearly constant. Once a plant or animal dies the Carbon is no longer being regenerated so the Carbon-14 starts to decay. By measuring the amount of Carbon-14 in the body of a prehistoric animal or plant, a scientist can deduce when the plant or animal died. Yet there are limits to this technique. The decay of Carbon-14 with half-life ℎ
h
can be modeled by the equation ()=0−
m
(
t
)
=
m
0
e
−
r
t
, where =ln(2)ℎ
r
=
ln
⁡
(
2
)
h
. It is known that Carbon-14 has a half-life of approximately 5730 years, and It's widely accepted that Carbon-14 dating is only accurate up to about 40,000 years.

What percentage of original Carbon-14 must be present for accurate testing?