Let us assume that the rate of decay follows a 1st
order reaction. Therefore the formula for rate of decay is:
A = Ao e^-kt --->
1
Where,
A = final value after time t
Ao = initial value at t zero
k = rate constant
t = time elapsed
First let use find for the value of constant k. We know
that the formula for half-life is:
t-half life = ln 2 / k
Finding for k:
5730 = ln 2 / k
k = 1.21 * 10^-4 yr^-1
Since it is stated that A = 0.00061 Ao, therefore
substituting all the values into equation 1:
0.00061 Ao / Ao = e^(-1.21 * 10^-4 yr^-1 * t)
Finding for t:
t = 61,173.98 years
The person died about 61,174 years ago.
