We can find k as follows :
Call the intial amt, C
And the amount left after 5730 yrs must be (1/2)C
So....we have this equation
(1/2)C = C * e ^(k * 5730)
(1/2) = e^(k * 5730) take the Ln of both sides
Ln (1/2) = Ln e ^(5730k) and we can write
Ln (1/2) = (5730k) Ln e [ Ln e = 1....so we can ignore this ]
So we have
Ln (1/2) = 5730 k divide both sides by 5730
Ln (1/2) / 5730 = k = Ln (.5) / 5730
So....to solve the problem ....we have that
.527 = e^(Ln (.5)/5730 * t) take the Ln of both sides
Ln (.527) = Ln e^( Ln(.5)/5730 * t)
Ln (.527) = Ln (.5)/5730 *t
t = Ln (.527) / [ Ln(.5) / 5730]
t = 5730 * Ln (.527) / Ln (.5) = 5295. 24 years old
So.....the man died @ absolute value [1991 - 5295.24] B.C. ≈ 3304.24 B. C. ≈ 3300 B. C.