The sample of fossilized wood is 22920 years old.
The half life is the time required for a substance to decay to half of its initial value. It is given by:
[tex]N=N_o(\frac{1}{2} )^\frac{t}{t_\frac{1}{2} }[/tex]
Where N is the final value of the substance, No is the initial value of the substance, t is the time and [tex]t_\frac{1}{2}[/tex] is the half life.
Given a half live of 5730 years, N = 1.5g, No = 24g. Hence:
[tex]1.5=24(0.5)^\frac{t}{5730} \\\\1/16=(0.5)^\frac{t}{5730} \\\\ln(1/16)=\frac{t}{5730} ln(0.5)\\\\t=22920\ years[/tex]
Therefore the sample is 22920 years old.
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