Carbon dating is a tool used to determine the age of a fossil. For example, a humanoid skull was found in a cave along with the remains of a campfire. Archaeologists believe the age of the skull to be the same as the campfire. 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 to reduce to half its initial amount. (a) Write an initial-value problem that models the amount of carbon-14 in the campfire. (b) If it is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire, find an explicit solution to the initial-value problem from part (a). Use the solution to estimate the age of the skull if the half-life of carbon-14 is about 5700 years.
Carbon dating is a tool used to determine the age of a fossil. For example, a humanoid skull was found in a cave along with the remains of a campfire. Archaeologists believe the age of the skull to be the same as the campfire. 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 to reduce to half its initial amount. (a) Write an initial-value problem that models the amount of carbon-14 in the campfire. (b) If it is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire, find an explicit solution to the initial-value problem from part (a). Use the solution to estimate the age of the skull if the half-life of carbon-14 is about 5700 years.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Carbon dating is a tool used to determine the age of a fossil. For example, a humanoid skull was found in a cave
along with the remains of a campfire. Archaeologists believe the age of the skull to be the same as the campfire.
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 to reduce to half its initial amount.
for part a I beleive that this is y'=ky where y is the amount of C14 and y(o) = y0 but I am probably wrong.
for part b I have no clue how to do this.
Transcribed Image Text:4. Carbon dating is a tool used to determine the age of a fossil. For example, a humanoid skull was found in a cave
along with the remains of a campfire. Archaeologists believe the age of the skull to be the same as the campfire.
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 to reduce to half its initial amount.
(a) Write an initial-value problem that models the amount of carbon-14 in the campfire.
(b) If it is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire,
find an explicit solution to the initial-value problem from part (a). Use the solution to estimate the age of the
skull if the half-life of carbon-14 is about 5700 years.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
