Question 48241
Your formula certainly works and your answer is essentially
correct.  I use a different formula for half-life problems.
For what it is worth I get:

0.59A = A(1/2)^(t/5730)
0.59 = (1/2)^(t/5730)
ln0.59 = (t/5730)(ln0.5)
t=5730[(ln0.59/ln0.5]
t= 4361.75 yrs.

Cheers,
Stan H.