Radioactive substances decay exponentially: The mass at time $t$ is $m(t)=m(0)e^{kt},$ where $m(0)$ is the initial mass and $k$ is a negative constant. The mean life M of an atom in the substance is $$M=-k \int_{0}^{\,\infty} {te^{kt}}\, dt.$$ For the radioactive carbon isotope, $^{14}$C, used in radiocarbon dating, the value of $k$ is -0.000121. Find the mean life of a $^{14}$C atom.

Make sure that your answer is correct to two decimal places.

$M =$