Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 70.3​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

The bones at the time they were​ discovered when the radioactive element​ carbon-14 has a​ half-life of total 5750 years are 10062.5-year-old.

What is half-lives?

Half lives is the time interval which is need to decay the atomic nuclei of a radioactive sample.

There is a scientist who determined that the bones from a mastodon had lost 70.3​% of their​ carbon-14.  Thus, the fraction remaining is,

f=1-(70.3/100)=1-0.703

f=1-(70.3/100)=0.297

Now the fraction remaining can be given as,

f=(1/2)ⁿ

Here, n is the half life elapsed. Put the value of fraction remaining.

0.297=(1/2)ⁿ

n=1.75

The radioactive element​ carbon-14 has a​ half-life of total 5750 years. Thus,

Years=1.75*5750

Years=10062.5

Thus, the bones at the time they were​ discovered when the radioactive element​ carbon-14 has a​ half-life of total 5750 years are 10062.5-year-old.

Learn more about the half lives here;

brainly.com/question/2320811

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