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4. a. Living matter (both human and non-human) absorbs carbon-14. When living matter dies, there is no longer absorption of carbon-14; and the amount of carbon- 14 very slowly diminishes in a dead object. However much carbon-14 is present in a dead object, it takes 5730 years for carbon-14 to diminish to half its value (i.e., the half-life of carbon-14 is 5730 years). The equation relating the number of carbon-14 atoms at two points in time is P = Pe", where t denotes time measured in years, P. denotes the number of atoms of Carbin-14 in an object when death occurs, and P, is the number of carbon-14 atoms t years later. [As an aside, and not needed to do this problem, P, is known because there is a relation between carbon-14 and carbon-12 (which does not deteriorate).] Find the yearly rate of decline r in carbon- 14 atoms. You should get a negative number because P,

4. a. Living matter (both human and non-human) absorbs carbon-14. When living matter dies, there is no longer absorption of carbon-14; and the amount of carbon- 14 very slowly diminishes in a dead object. However much carbon-14 is present in a dead object, it takes 5730 years for carbon-14 to diminish to half its value (i.e., the half-life of carbon-14 is 5730 years). The equation relating the number of carbon-14 atoms at two points in time is P = Pe", where t denotes time measured in years, P. denotes the number of atoms of Carbin-14 in an object when death occurs, and P, is the number of carbon-14 atoms t years later. [As an aside, and not needed to do this problem, P, is known because there is a relation between carbon-14 and carbon-12 (which does not deteriorate).] Find the yearly rate of decline r in carbon- 14 atoms. You should get a negative number because P,

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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4. a. Living matter (both human and non-human) absorbs carbon-14. When living matter dies, there is no longer absorption of carbon-14; and the amount of carbon- 14 very slowly diminishes in a dead object. However much carbon-14 is present in a dead object, it takes 5730 years for carbon-14 to diminish to half its value (i.e., the half-life of carbon-14 is 5730 years). The equation relating the number of carbon-14 atoms at two points in time is P = Pe¹¹, where t denotes time measured in years, P. denotes the number of atoms of Carbin-14 in an object when death occurs, and P, is the number of carbon-14 atoms t years later. [As an aside, and not needed to do this problem, P, is known because there is a relation between carbon-14 and carbon-12 (which does not deteriorate).] Find the yearly rate of decline r in carbon- 14 atoms. You should get a negative number because P < P b. How old is an object that now has 10% of the carbon-14 atoms that it had when it died?
Transcribed Image Text:4. a. Living matter (both human and non-human) absorbs carbon-14. When living matter dies, there is no longer absorption of carbon-14; and the amount of carbon- 14 very slowly diminishes in a dead object. However much carbon-14 is present in a dead object, it takes 5730 years for carbon-14 to diminish to half its value (i.e., the half-life of carbon-14 is 5730 years). The equation relating the number of carbon-14 atoms at two points in time is P = Pe¹¹, where t denotes time measured in years, P. denotes the number of atoms of Carbin-14 in an object when death occurs, and P, is the number of carbon-14 atoms t years later. [As an aside, and not needed to do this problem, P, is known because there is a relation between carbon-14 and carbon-12 (which does not deteriorate).] Find the yearly rate of decline r in carbon- 14 atoms. You should get a negative number because P < P b. How old is an object that now has 10% of the carbon-14 atoms that it had when it died?
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