The radioactive element carbon-14 has a half-life of 5750 years. a scientist determined that the bones from a mastodon had lost 67.7% of their carbon-14. how old were the bones at the time they were discovered?

The bones are 9370 years old at the time they were discovered.

The half-lives the sample has experienced:

Since 67.7% of the population has died, this indicates that 32.3 % of the population has survived.

So,

= -1.63039393

The value -1.63039393 indicates that there have been 1.63039393 half-lives since the mastodon perished.

This is true, according to a fast sanity check. Because only half of the carbon-14 would be left after one-half life.

After another half-life, there would be just 25% of the original carbon-14 left. And, because 32.3 percent falls between 25 and 50 percent, the estimate of 1.63 half-lives is appropriate.

Simply increase the number of half-lives wasted by the carbon-14 half-life.

1.63039393 5750 = 9374.765097 ≅ 9370 years

(by rounding to 3 significant figures)

Thus, the bones were 9370 years old at the time they were discovered.

Learn more about carbon dating, refer to the link:

link

it would be a gas formation