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A researcher claims that an ancient scroll originated from Greek scholars in about 500 BCE. A measure of its carbon-14 decay rate gives a value that is 89%% of that found in living organisms. How old is the scroll

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boffeemadrid

Answer:

[tex]963.34\ \text{years}[/tex]

Step-by-step explanation:

[tex]t_{1/2}[/tex] = Half life of carbon = 5730 years

[tex]\dfrac{N}{N_0}[/tex] = Decay rate = [tex]89\%=\dfrac{89}{100}[/tex]

Duration of time passed is given by

[tex]t=t_{1/2}\dfrac{\ln\dfrac{N}{N_0}}{\ln\dfrac{1}{2}}\\\Rightarrow t=5730\times\dfrac{\ln\dfrac{89}{100}}{\ln\dfrac{1}{2}}\\\Rightarrow t=963.34\ \text{years}[/tex]

The scroll is [tex]963.34\ \text{years}[/tex] old.

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