The graph shows the radioactive decay of a bone that is found to contain 1/8 of the carbon-14 found in living animals today.
Approximately how old is the bone?
a
5,730 years
b
11,460 years
c
22,920 years
d
17,190 years
The half-life of carbon-14 is 5,730 years. Since the bone contains 1/8 of the carbon-14 found in living animals today, we can determine that 3 half-lives have passed.
3 half-lives would be equal to 5,730 years x 3 = 17,190 years.
Therefore, the bone is approximately 17,190 years old.
The answer is d) 17,190 years.
To determine the approximate age of the bone, we need to consider the half-life of carbon-14. The half-life is the amount of time it takes for half of the radioactive material to decay.
The half-life of carbon-14 is approximately 5,730 years.
Since the bone contains 1/8 of the carbon-14 found in living animals today, it means that 7/8 of the carbon-14 has decayed (been lost) over time.
To find the age of the bone, we can use the fact that each half-life represents a 50% decrease in the amount of carbon-14.
Since 7/8 of the carbon-14 has decayed, this corresponds to approximately 3 half-lives.
Therefore, we can multiply the half-life of carbon-14 by the number of half-lives (3) to find the approximate age of the bone.
5,730 years * 3 = 17,190 years
Therefore, the approximate age of the bone is 17,190 years.
The answer is d) 17,190 years.
To determine the approximate age of the bone based on the graph of radioactive decay, we need to understand the concept of half-life. The half-life of a radioactive isotope, such as carbon-14, is the time it takes for half of the atoms in a sample to decay into a different element.
From the graph, we can see that the bone contains 1/8 of the carbon-14 found in living animals today. This means that 7/8 (or 1 - 1/8) of the carbon-14 has decayed.
The number of half-lives that have passed can be calculated using the formula:
Number of half-lives = Log(base 2) (Remaining amount / Initial amount)
In this case, the initial amount is 1, and the remaining amount is 7/8.
Number of half-lives = Log(base 2) (7/8)
Using a calculator, we can compute Log(base 2) (7/8) as approximately 0.125.
Since each half-life is approximately 5,730 years, the total age of the bone can be calculated as:
Approximate age = Number of half-lives * Half-life duration
Approximate age = 0.125 * 5,730 years
Approximate age = 716.25 years
Rounding to the nearest option, we can approximate the age of the bone to be 730 years.
Therefore, option a) 5,730 years is the closest approximation to the age of the bone.