The age of the fossil is 24, 312 years assuming an exponential decay model.
Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:
P = 100 e^(-kt)
Where P is the remaining quantity, k is the constant of decay, and t is time.
As the half life of the carbon 14 is 5700, when 50% of the substance remains,
50 = 100 e^(-5700k)
1/2 = e^(-5700k)
In(1/2) = In(e^(-5700k))
- In (2) = -5700k
k = In(2)/5700 = 0.0001216
Since, 5.2% carbon-14 remains,
5.2 = 100 e^(-0.0001216t)
0.052 = e^(-0.0001216t)
In(0.0052) = - 0.0001216
t = In(0.052) * - 0.0001216
t ≈ 24, 312 years.
Learn more about Exponential decay model:
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