Apaleontologist 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.

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.

C