Question

# The bones of a saber-toothed tiger are found to have an activity per gram of carbon...

The bones of a saber-toothed tiger are found to have an activity per gram of carbon that is 30.0% of what would be found in a similar live animal. How old are these bones?

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SOLUTION :

Radioactive carbon 14C has half-life of 5730 years.

So,

A / A0 = e^(- lamda * t)

=> 1/2 = e^(- lamda * 5730)

Taking ln :

=> ln(1/2) = - lamda * 5730

=> lamda = - ln(1/2) / 5730 = 1.20968 * 10^(-4)

So,

A(now) / A0 = e^(- 1.20968*10^(-4)  * t)

=> 0.30 =  e^(- 1.20968*10^(-4)  * t)

Takin ln :

=> ln(0.30) = - 1.20968*10^9-4) * t

=> t = ln(0.30) / (- 1.20968*10^(-4)

=> t =  9952.82 years

Hence, the bones are 9952.82 years old (ANSWER)

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