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Solved: In 23–27, assume that the rate of decay of a
Chapter 3, Problem 25E(choose chapter or problem)
Problem 25E
Problem
In Problems 23–27, assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of the substance to disintegrate.
Carbon dating is often used to determine the age of a fossil. For example, a humanoid skull was found in a cave in South Africa along with the remains of a campfire. Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire. Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.
Questions & Answers
QUESTION:
Problem 25E
Problem
In Problems 23–27, assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of the substance to disintegrate.
Carbon dating is often used to determine the age of a fossil. For example, a humanoid skull was found in a cave in South Africa along with the remains of a campfire. Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire. Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.
ANSWER:
Solution:-
Step1
Given that
We have to estimate the age of the skull if the half-life of carbon-14 is about 5600 years.
Step2
Let M(t) be the remaining original amount of carbon-14.
M(t)=2%=0.02
Let be the original amount of carbon-14.