The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5594 years. Suppose C'(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C' = k = (b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in 1988, according to these data? Age = years -kC. [1]: The New York Times, October 18, 1988.

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5594 years. Suppose C'(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C' = k = (b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in 1988, according to these data? Age = years -kC. [1]: The New York Times, October 18, 1988.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is
constantly replenished until the organism dies, after which it decays to stable carbon-12 at
a rate proportional to the amount of carbon-14 present, with a half-life of 5594 years.
Suppose C'(t) is the amount of carbon-14 present at time t.
(a) Find the value of the constant k in the differential equation C'=-kC.
k
=
(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to
be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14
contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in
1988, according to these data?
Age
=
years
[1]: The New York Times, October 18, 1988.

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