In digging a pond there got a bone, which has 80% of its initial carbon14. Using ✓ carbon decay model find the age of the bone.
Question
In digging a pond there got a bone, which has 80% of its initial carbon14. Using ✓ carbon decay model find the age of the bone.
Solution
The Carbon-14 decay model is represented by the equation:
N = N0 * e^(-0.000121 * t)
Where:
- N is the final amount of Carbon-14
- N0 is the initial amount of Carbon-14
- t is the time in years
- 0.000121 is the decay constant for Carbon-14
In this case, we know that N is 80% of N0. So we can set up the equation as follows:
0.8N0 = N0 * e^(-0.000121 * t)
We can simplify this by dividing both sides by N0:
0.8 = e^(-0.000121 * t)
To solve for t, we'll need to use natural logarithms. The equation becomes:
ln(0.8) = -0.000121 * t
Solving for t gives:
t = ln(0.8) / -0.000121
Using a calculator, we find that t is approximately 2230 years. So the bone is approximately 2230 years old.
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