Question

Carbon dating is used to determine the age of dead organic materials.The process uses radioactive carbon-14, which has half-life of around 6000 years.
Scientists are studying a mammoth found frozen in ice. They find that a sample of carbon from the remains has a count-rate of 200 counts per minute. When the mammoth died, the count-rate would have been 800 counts per minute. A second set of remains is found that are 18000 years older than the first set of remains. Calculate the count-rate of the second sample.

Answer 1

A(t)=A_0 exp⁡(-t/τ ln⁡2 )
Thus,
A(t+18000)=A_0 exp⁡(-(t+18000)/τ ln⁡2 )
A(t+18000)/A(t) =exp⁡(-18000/τ ln⁡2 )
A(t+18000)=200 exp⁡(-18000/6000 ln⁡2 )=25 counts per minute.
Answer: 25 counts per minute.