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The radioactive isotope carbon-14 is present 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 5598 years (half-life is how long it takes for half of the carbon-14 to decay). Suppose C(t) is the amount of carbon-14 present at time t. Find the value of the constant & in the differential equation C'=-kC. k= help (numbers) 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. In 1988 three teams according to these data? Age = years help (numbers) [1]: The New York Times, October 18, 1988.

The radioactive isotope carbon-14 is present 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 5598 years (half-life is how long it takes for half of the carbon-14 to decay). Suppose C(t) is the amount of carbon-14 present at time t. Find the value of the constant & in the differential equation C'=-kC. k= help (numbers) 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. In 1988 three teams according to these data? Age = years help (numbers) [1]: The New York Times, October 18, 1988.

Chemistry
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
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***Understanding Carbon-14 Decay: The Case of the Shroud of Turin*** The radioactive isotope carbon-14 is present in small quantities in all life forms and 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 5598 years (half-life is how long it takes for half of the carbon-14 to decay). Suppose \(C(t)\) is the amount of carbon-14 present at time \(t\). **Step 1: Determining the Decay Constant** Find the value of the constant \(k\) in the differential equation \(C' = -kC\): \[k = \_\_\_\_\_\] help (numbers) **Step 2: Estimating the Age of the Shroud of Turin** 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? \[Age = \_\_\_\_\_ \text{ years}\] help (numbers) --- [1]: *The New York Times*, October 18, 1988.
Transcribed Image Text:***Understanding Carbon-14 Decay: The Case of the Shroud of Turin*** The radioactive isotope carbon-14 is present in small quantities in all life forms and 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 5598 years (half-life is how long it takes for half of the carbon-14 to decay). Suppose \(C(t)\) is the amount of carbon-14 present at time \(t\). **Step 1: Determining the Decay Constant** Find the value of the constant \(k\) in the differential equation \(C' = -kC\): \[k = \_\_\_\_\_\] help (numbers) **Step 2: Estimating the Age of the Shroud of Turin** 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? \[Age = \_\_\_\_\_ \text{ years}\] help (numbers) --- [1]: *The New York Times*, October 18, 1988.
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