Uncertainty in Radioactive Decay Dating Calculation

[Granger]

Homework Statement

Charred wood remains were found in Conimbriga, probably with Roman origin. When measured at 14C activity in these remnants, it afforded 10.8 disintegrations per second per gram. The half-processing 14C is 5730 ± 30 years and the activity of this isotope in the atmosphere and in living matter is 13.5 disintegrations per second per gram.

Calculate the uncertainty in dating, because of the imprecision of 30 years in the half-transformation of 14C.

Homework Equations

N = No x e^(-kt)
R = Ro x e^(-kt)

R is the activity
k is the decay constant

The Attempt at a Solution

So there were previous question, one was calculating k (k = 1.21 x 10^-4) and the other was for calculate the dating (1844 years).
But now I have to calculate the uncertainty of the dating I previously calculated.
So, I know I need to derivate and use the propagation of errors formula... But I'm having trouble to get to the right expression...
The right answer of the problem is 10 years.

THANKS!

 

[gneill]

But now I have to calculate the uncertainty of the dating I previously calculated.
So, I know I need to derivate and use the propagation of errors formula... But I'm having trouble to get to the right expression...

Can you show your attempt?