Final answer:
To determine the age of a piece of wood using carbon-14 dating, calculate the number of half-lives that have occurred given the percentage of remaining carbon-14, and multiply by the half-life duration of 5730 years.
Step-by-step explanation:
The question involves calculating the age of a piece of wood based on the remaining percentage of carbon-14 (14C) compared to what is found in a living organism. The key to solving this problem is understanding the half-life of 14C, which is 5730 years. Given that the current carbon-14 content in the wood is 0.7813% of that in a living organism, we can use the concept of exponential decay to find the number of half-lives that have passed.
First, we need to determine how many half-lives would result in the wood having 0.7813% of the original 14C. The formula for decay is:
N(t) = N0 * (1/2)n
where N(t) is the remaining percentage of 14C, N0 is the initial percentage (100% for a living organism), and n is the number of half-lives.
By converting the percentage to a decimal (0.007813) and solving for n, we get:
n = log(N(t)/N0) / log(1/2)
n = log(0.007813/1) / log(1/2) = log(0.007813) / log(0.5)
By calculating the logarithms, we can solve for the number of half-lives and then multiply by the half-life duration (5730 years) to find the age of the sample.