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Multiple Choice
What percentage of carbon – 14 ( t1/2 = 5715 years) remains in a sample estimated to be 18,315 years old?
A
11.09%
B
27.96%
C
18.72%
D
10.85%
Verified step by step guidance
1
Identify the given information: the half-life (t1/2) of carbon-14 is 5715 years, and the age of the sample is 18,315 years.
Use the formula for radioactive decay: N(t) = N0 * (1/2)(t/t1/2), where N(t) is the remaining quantity of the substance, N0 is the initial quantity, t is the time elapsed, and t1/2 is the half-life.
Substitute the given values into the formula: N(t) = N0 * (1/2)(18,315/5715).
Calculate the exponent: (18,315 / 5715) to determine how many half-lives have passed.
Determine the remaining percentage of carbon-14 by evaluating the expression (1/2)(18,315/5715) and converting it to a percentage by multiplying by 100.