A specimen has .625 the amount of carbon 14 you would find in a living specimen.
How many half-lives has the specimen been through?
How old is the specimen?
.5^n = .625
n ln .5 = ln .625
n = -.470/-.693 = 0.678 half lives
.678*5730 = 3885 years
To determine the number of half-lives the specimen has been through, we need to use the equation:
N = N0 * (1/2)^(n),
where N is the current amount of carbon 14 in the specimen, N0 is the initial amount of carbon 14 in a living specimen, and n is the number of half-lives. We are given that the specimen has 0.625 the amount of carbon 14 in a living specimen.
Let's substitute the given values into the equation:
0.625 = 1 * (1/2)^(n)
To solve for n, we can take the logarithm of both sides (base 2):
log2(0.625) = log2(1/2)^(n)
log2(0.625) = n * log2(1/2)
Using the rule of logarithms, we can rewrite the equation as:
log2(0.625) = -n
Now, we can solve for n by dividing both sides by -1:
n = -log2(0.625)
Using a calculator, we find:
n ≈ 3.3219
Since we can't have a fractional number of half-lives, we need to round the answer to the nearest whole number. Therefore, the specimen has been through approximately 3 half-lives.
To determine the age of the specimen, we need to know the half-life of carbon 14. The half-life of carbon 14 is approximately 5730 years.
To calculate the age, we multiply the number of half-lives by the half-life of carbon 14:
Age = Number of half-lives * Half-life of carbon 14
Age = 3 * 5730
The age of the specimen is approximately 17,190 years.