he 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
17,190 years
d
22,920 years
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 can be inferred that it has undergone 3 half-lives (1/2 * 1/2 * 1/2 = 1/8). Therefore, the approximate age of the bone is 5,730 years * 3 = <<5730*3=17190>>17,190 years. The answer is c) 17,190 years.
To determine the approximate age of the bone, we can use the concept of half-life. The half-life of carbon-14 is approximately 5730 years.
Given that the bone contains 1/8 of the carbon-14 found in living animals today, we can calculate the number of half-lives that have occurred.
1/8 is equal to (1/2)^(n), where n is the number of half-lives.
Taking the logarithm of both sides, we have:
log(1/8) = log((1/2)^(n))
log(1/8) = n * log(1/2)
n = log(1/8) / log(1/2)
Using a calculator, we can evaluate the expression:
n ≈ -3 / -0.301 = 9.9661
Since we can't have a fraction of a half-life, we round the value to the nearest whole number. Therefore, approximately 10 half-lives have occurred.
To determine the age, we multiply the number of half-lives by the half-life of carbon-14:
Age ≈ 10 * 5730 years
Age ≈ 57,300 years
Therefore, the approximate age of the bone is 57,300 years.
None of the available options match the calculated age. It is possible that there is an error in the data or options provided.
To determine the approximate age of the bone, we need to understand the radioactive decay of carbon-14 and its half-life.
Carbon-14 is a radioactive isotope of carbon that is present in the atmosphere and taken in by living organisms. It undergoes radioactive decay over time, with a half-life of approximately 5,730 years. This means that after 5,730 years, half of the carbon-14 in a sample will have decayed.
In this scenario, the bone is found to contain 1/8 of the carbon-14 found in living animals today. If we assume that the amount of carbon-14 in living animals today is 100% (or 8/8), then 1/8 of this amount is left in the bone.
Since each half-life reduces the amount of carbon-14 by half, we can determine how many half-lives it takes to reach 1/8 of the original amount.
1/8 = (1/2)^(n)
Where n represents the number of half-lives.
To solve for n, we can take the logarithm of both sides:
log(1/8) = n * log(1/2)
Using logarithmic properties, we know that log(1/2) is approximately -0.3010.
log(1/8) = -0.3010n
log(8) = 0.3010n
Simplifying, we find:
n = log(8) / 0.3010
n ≈ 3
Therefore, it takes approximately 3 half-lives for the bone to contain 1/8 of the original carbon-14.
To find the age of the bone, we multiply the half-life (5,730 years) by the number of half-lives:
Age of the bone ≈ 3 * 5,730 years
Age of the bone ≈ 17,190 years
Therefore, the approximate age of the bone is c) 17,190 years.