Question

archeologists use radiocarbon dating to determine he age of ancient tools. they measure levels of the isotope carbon-14, which has a half life of 5,730 years. Which function models the decay of carbon-14? answer: B

Answer 1

B

Explanation:

edg2020

Answer 2

Option (2)

Explanation:

Formula to determine the final amount of an element after t years is,

`A_t=A_0e^(kt)`

where
`A_t` = Final amount

`A_0` = Initial amount

t = Duration or time

k = decay constant

If the half life period of a C-14 isotope = 5730 years

`A_t=(A_0)/(2)` [For half life period]

`(A_0)/(2)=A_0e^((5730)k)`

`e^(5730k)=0.5`

`\text{ln}(e^(5730k))=\text{ln}(0.5)`

0.5730k = -0.6931

k =
`-(0.6931)/(5730)` = -0.000121

Therefore, formula for the radioactive decay will be.

`A_t=A_0e^(-0.000121t)`

Option (2) will be the answer.