SOLUTION: A radioactive substance decays from 20 pounds to 19.9 pounds in 25 years. approximate the half life of the substance,

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Question 325438: A radioactive substance decays from 20 pounds to 19.9 pounds in 25 years. approximate the half life of the substance,
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
N=N0%2Ae%5E%28kt%29
Find k.
19.9=20%2Ae%5E%28k%2825%29%29
e%5E%2825k%29=19.9%2F20
25k=ln%2819.9%2F20%29
k=ln%2819.9%2F20%29%2F25
.
.
.
Now find the half life.
N0%2F2=N0%2Ae%5E%28kt%29
kt=ln%281%2F2%29
t=ln%281%2F2%29%2Fk
t=%2825%2Aln%281%2F2%29%29%2F%282%2Aln%2819.9%2F20%29%29
t=1728.5
The half life is 1728.5 years.