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)
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Chapter1: Combinatorial Analysis
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fb69d79-3cfd-4273-ad7c-eba8454eb709%2F96acb00f-cf55-4dcf-b09f-a9550d8bfb7b%2Fyzwjggc_processed.png&w=3840&q=75)
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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