An anthropologist finds bone that her instruments measure it as 0.717% of the amount of carbon-14 the bones would have contained

Question

3 years ago

8

An anthropologist finds bone that her instruments measure it as 0.717% of the amount of carbon-14 the bones would have contained

when the person was alive. How long ago did the person die? The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand .
****PLEASE HELP****

Mathematics

1 answer:

ExtremeBDS [4] · Answer 1 · 2021-12-01T13:02:50+03:00

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.