#### Answer

This is a writing exercise for the student, and answers will vary.

#### Work Step by Step

Sample 1:
The half-life of carbon-14 is 5730 years. If a plant were to die today, what fraction of the carbon-14 atoms now present in its cells will have decayed, 11460 years from now?
a. $\frac{1}{2}$
b. $\frac{1}{4}$
c. $\frac{3}{4}$
d. $\frac{1}{8}$
The correct answer is C, three-quarters.
After one half-life, at t = 5730 years, we are down to one-half the original amount of C-14. Half of the present atoms have decayed.
After two half-lives, at t = 11460 years, we are down to one-quarter the original amount of C-14. That means that 1 - 0.25 = 0.75 of the original C-14 atoms have decayed.
Sample 2:
Atoms of AAA decay to atoms of BBB with a half-life of 10,000 years. A sample starts with 200,000 atoms of AAA (and none of BBB). After how long will there be only 25,000 atoms of AAA?
a. 20,000 years
b. 3,333 years
c. 30,000 years
d. 2,500 years
The correct answer is C, or 30,000 years.
25,000 is one-eighth of 200,000.
After one half-life, at t = 10000 years, we are down to one-half the original amount of AAA.
After two half-lives, at t = 20000 years, we are down to one-quarter the original amount of AAA.
After three half-lives, at t = 30000 years, we are down to one-eighth the original amount of AAA.
This is discussed on page 625.