14. Radioactive Radium The half-life of radium-226 is 1600 years. Suppose we have a 22-mg sample. (a) Find a function that models the mass remaining after t years. Exbicza (b) How much of the sample will remain after 4000 years! (c) After how long will only 18 mg of the sample remain!

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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tion
hour. When a certain critical number of bacteria are present
Look up
California's
actual population in 2000, and compare.
13. Infectious Bacteria An infectious strain of bacteri.
increases in number at a relative growth rate of 200%
per
in the bloodstream, a person becomes ill. If a single
bacterium infects a person, the critical level is reached in
24 hours. How long will it take for the critical level to be
reached if the same person is infected with 10 bacteria?
14-22 - These exercises use the radioactive decay model.
14. Radioactive Radium The half-life of radium-226 is 1600
years. Suppose we have a 22-mg sample. a
(a) Find a function that models the mass remaining after
t years.
(b) How much of the sample will remain after 4000 years?
(c) After how long will only 18 mg of the sample remain!
15. Radioactive Cesium The half-life of cesium-137 is
30 years. Suppose we have a 10-g sample.lugot da
(a) Find a function that models the mass remaining atfter
t years.
(b) How much of the sample will remain after 80 years.
(c) After how long will only 2 g of the sample remain?
g aftert
16. Radioactive Thorium The mass m(t)
days from a 40-g sample of thorium-23
-0.027
m(t)
40e
Hou muoh of the sample will re
ays?
(o)
Transcribed Image Text:tion hour. When a certain critical number of bacteria are present Look up California's actual population in 2000, and compare. 13. Infectious Bacteria An infectious strain of bacteri. increases in number at a relative growth rate of 200% per in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 24 hours. How long will it take for the critical level to be reached if the same person is infected with 10 bacteria? 14-22 - These exercises use the radioactive decay model. 14. Radioactive Radium The half-life of radium-226 is 1600 years. Suppose we have a 22-mg sample. a (a) Find a function that models the mass remaining after t years. (b) How much of the sample will remain after 4000 years? (c) After how long will only 18 mg of the sample remain! 15. Radioactive Cesium The half-life of cesium-137 is 30 years. Suppose we have a 10-g sample.lugot da (a) Find a function that models the mass remaining atfter t years. (b) How much of the sample will remain after 80 years. (c) After how long will only 2 g of the sample remain? g aftert 16. Radioactive Thorium The mass m(t) days from a 40-g sample of thorium-23 -0.027 m(t) 40e Hou muoh of the sample will re ays? (o)
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