SOLUTION: An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y

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Question 966341: An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0ekt that models the situation, give the exact value of k in terms of natural logarithms: y0 = 20 mg; the half-life is 200 days.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units.
For an equation of the form y = y0ekt that models the situation, give the exact value of k in terms of natural logarithms: y0 = 20 mg; the half-life is 200 days.
:
The equation is:
Half remains after 200 days
Y+=+Yo%2Ae%5E%28kt%29 where:
Y = amt after t time (10 mg)
Yo = initial amt (20 mg)
k = half-life of the substance
t = time of decay (200)
:
20%2Ae%5E%28200k%29+=+10
e%5E%28200k%29+=+10%2F20
e%5E%28200k%29+=+1%2F2
ln of e is 1, therefore
200k+=+ln%281%2F2%29
200k = -.693147
k = -.693147%2F200
k = -.0034657
:
:
Check this on your calc: 20*e^(-.0034657*200) = 10.000