Exercise 70 Page 537

First, we will determine the equation of decay for Carbon-14. Then we will use it to answer the given question.

Equation of Decay for Carbon-14

We will use the exponential decay formula to determine the equation of decay for Carbon-14. y=ae^(- kt)Here, a is the initial value, t is time in years, and k is a constant representing the rate of continuous decay. To determine the equation of decay for Carbon-14, we have to find the value of k. We know that the half-life of Carbon-14 is 5760 years. It means that when t=5760 y is equal to the half of the initial value, y=0.5a.

We have that k is about 0.00012. We can write the equation of decay for Carbon-14. y=ae^(- 0.00012t)

How Long Ago Did The Person Die?

We know that the bones contain less than 0.5 % of the amount of Carbon-14 they would have contained when the person was alive. In other words, after t years the bones contain less than 0.005 of the initial amount a of Carbon-14. Let's substitute 0.005a for y into the equation of decay for Carbon-14. 0.005a=ae^(- 0.00012t) We want to find the value of t, so let's solve the above equation.

The person died about 44 153 years ago.