SOLUTION: A lab has 50 mg sample os cobalt-60, which decays at the continous yearly rate of 13%. A) Find a function R(t) that gives the number of mg present as a function of time in years. B

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Question 610059: A lab has 50 mg sample os cobalt-60, which decays at the continous yearly rate of 13%. A) Find a function R(t) that gives the number of mg present as a function of time in years. B) How much of the sample will remain after 10 years? C) What is the half-life of the element?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A lab has 50 mg sample of cobalt-60, which decays at the continuous yearly rate of 13%.
A) Find a function R(t) that gives the number of mg present as a function of time in years.
R(t) = 50%2A%281-.13%29%5Et
:
B) How much of the sample will remain after 10 years?
R(10) = 50%2A%281-.13%29%5E10
put this in your calc
R(10) = 12.42 mg
:
C) What is the half-life of the element?
50%2A%281-.13%29%5Et = 25
.87%5Et = 25%2F50
using nat logs
t%2Aln%28.87%29+=+ln%28.5%29
:
t = ln%28.5%29%2Fln%28.87%29
t = 4.98 yrs, half-life