Question

A paleontologist uncovers a fossil of a saber-toothed cat in California. He analyzes the fossil and concludes that the specimen contain 15% of its original carbon-14. Carbon-14 has a half-life of 5730 years. Use carbon-14 dating to determine the age of the fossil.

Answer 1

Carbon-14 dating is used to determine the age of fossils by comparing the amount of carbon-14 in the specimen to the amount in the atmosphere. The half-life of carbon-14 is 5730 years, and by analyzing the percentage of carbon-14 remaining, the age of the fossil can be calculated.

Step-by-step explanation:

Carbon-14 dating is used to determine the age of fossils. Carbon-14 (14C) is a radioisotope that is present in living organisms while they are alive, and it starts to decay after they die. The half-life of carbon-14 is 5730 years, which means that after this time period, half of the original carbon-14 will have decayed.

In the case of the saber-toothed cat fossil, the paleontologist analyzed the specimen and found that it contained 15% of its original carbon-14. By comparing this percentage to the amount of carbon-14 in the atmosphere, which is known, they can determine the age of the fossil.

Since carbon-14 dating is accurate up to about 50,000 years, this method is suitable for dating the fossil. The age of the fossil can be calculated by considering the amount of carbon-14 remaining and the known half-life of the isotope.

Answer 2

Answer: 15,682 years

To find this, start with the half-life formula and fill in the values you know.

It will be:

15 = 100 (0.5) ^ (x/5730)

To solve it, you can divide both sides by 100. Then, take the log of each side. This will allow you to bring the x out of the exponent.

You will have:

log(0.15)=(x/5730) log(0.5)

Divide both sides by log(0.5) and multiply by 5730.
You will get 15,683 years.