While exploring a coal mine, scientists found plant fossils in the ceiling of the mine which had been preserved by an earthquake. Samples taken from one of the fossils have carbon$-14$ activities of $40\mathrm{.}0$ counts $\frac{?}{\text{m}\text{i}\text{n}}.$ A reference sample of the same size, from a plant alive today, has a carbon$-14$ activity of $160\mathrm{.}0$ counts $\frac{?}{\text{m}\text{i}\text{n}}.$

Carbon$-14$ has a half$-$life of $5730$ years: what is the age of the plant fossils in years?