Solving for r in Carbon-14's Half-Life

[TG3]

Homework Statement
The half life of carbon 14 is 5730 years long. Assume that dQ/dt = -rQ. Determine the constant rate r.

The attempt at a solution

dQ/dt = -rQ (Given)

dQ/Q = -rdt (algebra)
lnQ = -rt (integrate)
-lnQ/t = r (algebra)

How do I work in 5,730? Also, did I do the equations correctly?

 

[lanedance]

I think you have forgotten a constant in your inetgration if it is an indefinite integral, otherwise integration looks ok

to get r
start with Q = 1 at t = 0
then by the meaning of half life, you have Q = 1/2 at t = 5730yrs

Another option is to re-perform the integration as a definite integral from t=0 to t= 5730 knowing the Qf/Qi ratio = 1/2