So I have an exercise that says that the initial rate of $14\mathrm{C}$ was $13.5$ (per second) and nowadays it $10.8$ (per second). The half-life time is $5730$ years with an uncertainty of $30$ years... Then it's asked to calculate the decay constant ($-1.21 \times 10^-4 \,\mathrm{(year)^{-1}}$) and the time that has passed since the carbon was set free ($1844$ years).
Now it's asked to calculate the uncertainty in the calculation of the time.
I'm having trouble deriving the expressions that allow me to calculate the uncertainty... Can someone help me?
Thanks!
EDIT:
For calculate the uncertainty I need do derivate the formula $t = -\frac{A}{k}$
BUT I also need to multiply this by the uncertainty of $k$
So I need to calculate the uncertainty of $k$
How can I do it?