The age of an ancient tree trunk is estimated using radiocarbon dating. If the trunk has a C-14 decay rate that is 34% of what it is in living plants, how old is the trunk?
The half-life of C-14 is 5730 years.
The half-life of C-14 is 5730 years.
1 Answer
I got
Explanation:
I'm assuming that you are saying that there is only
We have to use the half-lives of carbon to calculate the age, as well as the fraction remaining.
Know that, after
(Source: https://en.wikipedia.org/wiki/Half-life)
So, we can setup the following equation:
Removing percent from both sides, we get
From here, cross multiplication gives us
Now, we have to use logarithms. We can take the natural log of both sides, which yields
Using the power rule for logarithms,
Now, we can divide by
From here, we need to use a calculator to figure out the answer. Plugging this into a calculator, it gives us
So, the carbon-14 in the trunk has elapsed
I hope that my explanation was clear! Feel free to ask me anything in the comments or send me a message.