Respuesta :
9370 years
First, you need to determine how many half-lives the sample has undergone. Since 67.7% has been lost, that means that 100% - 67.7% = 32.3% has been retained. So calculate the logarithm to base 2 of 0.323:
log(0.323)/log(2) = -0.490797478/0.301029996 = -1.63039393
The number -1.63039393 tells you that 1.63039393 half-lives have occurred since the mastodon died. A quick sanity check will assure you that this is true. Because after 1 half live, there would be 50% of the carbon-14 remaining. And after another half life, there would be 25% of the original carbon-14 remaining. And since 32.3% is between 25% and 50%, the value of 1.63 half lives is quite reasonable. Now just multiply the number of half lives expended by the half life of carbon-14.
1.63039393 * 5750 = 9374.765097
Rounding to 3 significant figures gives us 9370 years.
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, [tex]\rm \dfrac{log(0.323)}{log(2) } = \dfrac{-0.490797478}{0.301029996}[/tex]
= -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 [tex]\times[/tex] 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:
https://brainly.com/question/18945700
