How do you calculate c14 dating?

Carbon 14 is a common form of carbon which decays over time. The amount of Carbon 14 contained in a preserved plant is modeled by the equation f(t) = 10e^{-ct}.

Whats the greatest age that a thing can be to be able to be dated by carbon 14?

40,000 years old Carbon-14 dating can determine the age of an artifact that is up to 40,000 years old.