How many years old is the artifact?
Question. A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.
A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of carbon-14 is 5730 years.)
How to find and solve this question?
I don't know how to calculate and to find this correct formula?
- PuzzlingLv 74 weeks ago
I'm assuming you are asking about the half-life problem and we should ignore the iodine-125 part?
First, let's think a little about what we expect in terms of a solution.
The half life is 5730 years. So after 5730 years, we would expect to have 50 percent of the carbon-14. We instead have 60 percent, so it hasn't gone through a full half life period. The answer will be less than 5730 years, right?
The formula for the amount of material after t years is:
A(t) = Ao * (1/2)^(t/λ)
Ao : Initial amount
A(t) : Amount at time t (in years)
t : time (in years)
λ : half-life (in years)
So for your case, you have:
0.6 * Ao = Ao * (1/2)^(t/5730)
You can cancel the original amount from both sides:
0.6 = (1/2)^(t/5730)
Now take the log of both sides:
log(0.6) = log((0.5)^(t/5730))
Use this rule of logs --> log(a^b) = b log(a)
log(0.6) = t/5730 * log(0.5)
Solve for t:
t = 5730 log(0.6) / log(0.5)
I'll leave the final calculation to you. Round accordingly.
- BryceLv 74 weeks ago
k=ln0.50 /5730≈ -0.000121
t= ln0.60 /-0.000121≈ 4223 years