Solve the problem.
-A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays
According to the equation .
A) 15,000 years
B) 150 years
C) 15,035 years
D) 1,500 years

Question

Solve the problem.
-A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays
According to the equation  .
A) 15,000 years 
B) 150 years 
C) 15,035 years 
D) 1,500 years

Quizplus · Accepted Answer

Carbon-14 decays at a rate of approximately 5730 years, which is known as its half-life. Therefore, we can use the formula for exponential decay, which is:
y = a(1/2)^(t/h)
where y is the remaining amount, a is the initial amount, t is the time elapsed, and h is the half-life. We know that y/a = 15.5% = 0.155, and h = 5730 years. Solving for t, we get:
0.155 = 1(1/2)^(t/5730)
taking the natural logarithm of both sides
ln(0.155) = (t/5730)ln(1/2)
t = 5730ln(0.155)/ln(1/2) 
t = 15,035 years, which is closest to choice C. Based on the percentage of carbon-14 remaining, we can use the half-life of carbon-14 which is known to be approximately 5,700 years. Using the formula for exponential decay, we can estimate the age of the fossil bone to be approximately 15,035 years. Therefore, the best choice is C.

Solve the Problem. -A Carbon-14 Dating Test Is Performed on a Fossil Bone