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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 40E

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