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A fossilized leaf contains 15% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

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meerkat18
To determine the amount of substance left (At) in t years we use,
                                 At = (Ao) x e^-kt
where Ao is the initial amount and k is the constant. Substituting the given half-life
                                At / Ao = 0.5 = e^-k(5600)
The value of k is 1.2377x10^-4
Using the same equation,
                                At / Ao = 0.15 = e^-(1.2377x10^-4)(t)
The value of t is 15327. Thus, the fossil is approximately 15327 years old.
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