You are assisting in an anthropology lab over the summer by carrying out \({ }^{14} \mathrm{C}\) dating. \(\mathrm{A}\) graduate student found a bone he believes to be 20,000 years old. You extract the carbon from the bone and prepare an equal-mass sample of carbon from modern organic material. To determine the activity of a sample with the accuracy your supervisor demands, you need to measure the time it takes for 10,000 decays to occur.
a. The activity of the modern sample is \(1.06 \mathrm{~Bq}\). How long does that measurement take?
b. It turns out that the graduate student's estimate of the bone's age was accurate. How long does it take to measure the activity of the ancient carbon?