SOLUTION: A radioactive substance has a half-life of T hours. If after 4.6 hours, 12.6 kg. remain form an initial amount of 20 kg. What is the half-life to the nearest tenth of an hour?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A radioactive substance has a half-life of T hours. If after 4.6 hours, 12.6 kg. remain form an initial amount of 20 kg. What is the half-life to the nearest tenth of an hour?       Log On


   

Question 324778: A radioactive substance has a half-life of T hours. If after 4.6 hours, 12.6 kg. remain form an initial amount of 20 kg. What is the half-life to the nearest tenth of an hour?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
N=N0%2Ae%5E%28kt%29
12.6=20e%5E%284.6k%29
e%5E%284.6k%29=12.6%2F20=0.63
4.6k=ln%280.63%29
k=ln%280.63%29%2F4.6
k=-0.100
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For half life,
kt=ln%281%2F2%29
t=ln%281%2F2%29%2F%28-0.100%29
t=6.9 hrs.
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The half life is 6.9 hrs.