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.
