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The half-life of Carbon-14 is about 5730 years. This means that it takes approximately 5730 years for any amount of Carbon-14 to decay to half of the original amount. Suppose you analyze an artifact weighing 1200 grams. (a) Write a recurrence relation for the amount of Carbon 14 left in the object after n periods of time, where each period is 5730 years. (b) Solve the recurrence relation. (c) How much Carbon-14 will be left in the object after 57,300 years?

The half-life of Carbon-14 is about 5730 years. This means that it takes approximately 5730 years for any amount of Carbon-14 to decay to half of the original amount. Suppose you analyze an artifact weighing 1200 grams. (a) Write a recurrence relation for the amount of Carbon 14 left in the object after n periods of time, where each period is 5730 years. (b) Solve the recurrence relation. (c) How much Carbon-14 will be left in the object after 57,300 years?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. The half-life of Carbon-14 is about 5730 years. This means that it takes approximately 5730 years for any amount of Carbon-14 to decay to half of the original amount. Suppose you analyze an artifact weighing 1200 grams. (a) Write a recurrence relation for the amount of Carbon 14 left in the object after n periods of time, where each period is 5730 years. (b) Solve the recurrence relation. (c) How much Carbon-14 will be left in the object after 57,300 years?
Transcribed Image Text:5. The half-life of Carbon-14 is about 5730 years. This means that it takes approximately 5730 years for any amount of Carbon-14 to decay to half of the original amount. Suppose you analyze an artifact weighing 1200 grams. (a) Write a recurrence relation for the amount of Carbon 14 left in the object after n periods of time, where each period is 5730 years. (b) Solve the recurrence relation. (c) How much Carbon-14 will be left in the object after 57,300 years?
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5. The half-life of Carbon-14 is about 5730 years. This means that it takes approximately 5730 years for any amount of Carbon-14 to decay to half of the original amount. Suppose you analyze an artifact weighing 1200 grams. (a) Write a recurrence relation for the amount of Carbon 14 left in the object after n periods of time, where each period is 5730 years. (b) Solve the recurrence relation. (c) How much Carbon-14 will be left in the object after 57,300 years?
Transcribed Image Text:5. The half-life of Carbon-14 is about 5730 years. This means that it takes approximately 5730 years for any amount of Carbon-14 to decay to half of the original amount. Suppose you analyze an artifact weighing 1200 grams. (a) Write a recurrence relation for the amount of Carbon 14 left in the object after n periods of time, where each period is 5730 years. (b) Solve the recurrence relation. (c) How much Carbon-14 will be left in the object after 57,300 years?
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