A cypress beam found in the tomb of Sneferu in Egypt contained 55% of the radioactive carbon-14 (C-14) that is found in living cypress wood. It is well-known that the half life of C-14 is approximately 5,600 years. (a) Write the initial-value problem that models this scenario using an appropriate differential equation and initial condition. (b) Show that the general solution of the IVP from part a) is given by A(t) = Cekt, where A(t) is the amount of radioactive C-14 at any time t, and determine the particular solution. (c) Determine the approximate age of the tomb. For your answer, use a complete statement and appropriate units.
A cypress beam found in the tomb of Sneferu in Egypt contained 55% of the radioactive carbon-14 (C-14) that is found in living cypress wood. It is well-known that the half life of C-14 is approximately 5,600 years. (a) Write the initial-value problem that models this scenario using an appropriate differential equation and initial condition. (b) Show that the general solution of the IVP from part a) is given by A(t) = Cekt, where A(t) is the amount of radioactive C-14 at any time t, and determine the particular solution. (c) Determine the approximate age of the tomb. For your answer, use a complete statement and appropriate units.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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Question
A cypress beam found in the tomb of Sneferu in Egypt contained 55%
of the radioactive carbon-14 (C-14) that is found in living cypress wood. It is
well-known that the half life of C-14 is approximately 5,600 years.
(a) Write the initial-value problem that models this scenario using an appropriate
differential equation and initial condition.
(b) Show that the general solution of the IVP from part a) is given by A(t) = Cekt,
where A(t) is the amount of radioactive C-14 at any time t, and determine the
particular solution.
(c) Determine the approximate age of the tomb. For your answer, use a complete
statement and appropriate units.
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