SOLUTION: A certain radioactive substance decays according to the formula q(t)= q0e^-.0063t. where q0 is the initial amount of the substance and t is the time in days. Approximate the half-l

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A certain radioactive substance decays according to the formula q(t)= q0e^-.0063t. where q0 is the initial amount of the substance and t is the time in days. Approximate the half-l      Log On


   

Question 867851: A certain radioactive substance decays according to the formula q(t)= q0e^-.0063t. where q0 is the initial amount of the substance and t is the time in days. Approximate the half-life of the substance.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A certain radioactive substance decays according to the formula q(t)= q0e^-.0063t. where q0 is the initial amount of the substance and t is the time in days. Approximate the half-life of the substance.
:
let Qo = 1, then Q(t) = .5
A simple equation
1%2Ae%5E%28-.0063t%29+=+.5
find the ln of both sides
ln%28e%5E%28-.0063t%29%29+=+ln%28.5%29
the log equiv of exponents
-.0063t*ln(e) = ln(.5)
the ln of e is one so we have
-.0063t = -.693147
t = %28-.693147%29%2F%28-.0063%29
t = +110 days is the half life of the substance