11,460 years
To find the age of the organism, we can use the formula for exponential decay:
A(t) = A(0) * (1/2)^(t/T)
Where:
A(t) = the amount of carbon-14 remaining after time t
A(0) = the initial amount of carbon-14
t = time elapsed
T = half-life of carbon-14 (5,730 years)
We are given that the organism has 25% of the total amount of atmospheric C-14 remaining. Therefore, A(t) = 0.25.
0.25 = (1/2)^(t/5730)
Taking the natural logarithm of both sides:
ln(0.25) = ln((1/2)^(t/5730))
ln(0.25) = (t/5730) * ln(1/2)
ln(0.25) = (t/5730) * -ln(2)
t = 5730 * ln(0.25) / -ln(2)
Calculating this out:
t ≈ 11,460 years
Therefore, the age of the organism is approximately 11,460 years.
Carbon-14 is used to determine the time an organism was living. The amount of carbon-14 an organism has is constant with the atmosphere, but when an organism dies the carbon-14 decays at a half-life of 5,730 years. If an archeologist measured the amount of carbon-14 in an organism and it was 25% of the total amount of atmospheric C-14, what is the age of the organism?
1432.5 years
5,730 years
11,460 years
17,190 years
1 answer
3 answers