The relationship for radioactive decay is given by:
N(t) = N₀ * exp(-kt), where k is the decay constant.
We may substitute k using the equation:
k = 0.693 / t₀.₅, where t₀.₅ is the half life of the substance
The equation becomes:
N(t) = N₀ * exp(-0.693t / t₀.₅)
The ratio of N(t) : N₀ is 0.717%, or 0.00717. Using this
0.00717 = exp(-0.693t / 5,730)
0.693t = 28,294
t = 40,828.3
The person was alive almost 41,000 years ago.
