The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are present in a given sample. Half of the original number of radioactive nuclei have undergone disintegration in a period of 1500 4.- years. Assuming that Q satisfies the differential equation Q' = -rQ, find an expression for Q(t) at any time t, if Q(0) = Qo- (Show all steps.) b) a) What percentage of the original radioactive nuclei will remain after 4500 years?

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The rate at which radioactive nuclei decays is proportional to the
number of such nuclei that are present in a given sample. Half of the original
number of radioactive nuclei have undergone disintegration in a period of 1500
4.-
years.
а)
Assuming that Q satisfies the differential equation Q' = -rQ, find an
expression for Q(1) at any time t, if Q(0) = Qo- (Show all steps.)
b)
What percentage of the original radioactive nuclei will remain after 4500
years?
Transcribed Image Text:The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are present in a given sample. Half of the original number of radioactive nuclei have undergone disintegration in a period of 1500 4.- years. а) Assuming that Q satisfies the differential equation Q' = -rQ, find an expression for Q(1) at any time t, if Q(0) = Qo- (Show all steps.) b) What percentage of the original radioactive nuclei will remain after 4500 years?
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