A scientist would measure the amount of carbon-14 (¹⁴C) in a fossil to determine its age.
The ¹⁴C:¹²C ratio is constant in living organisms. When they die, the radioactive ¹⁴C decays, so the ratio changes. The half-life for the for the decay is 5730 a, so scientists can work backwards and calculate how long ago the plant died. The method is good for determining the age of fossils up to 50 000 a old.