SOLUTION: The half-life of a certain substance is 27. How long will it take for a sample of this substances to decay to 88% of it original amount? Use exponential decay model to solve. {{{A=

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The half-life of a certain substance is 27. How long will it take for a sample of this substances to decay to 88% of it original amount? Use exponential decay model to solve. {{{A=      Log On


   

Question 857664: The half-life of a certain substance is 27. How long will it take for a sample of this substances to decay to 88% of it original amount? Use exponential decay model to solve. A=Aoe%5E%28kt%29
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Stating the time units for the half-life would be a good thing to do.

A quantity, I, of the substance drops to I/2 in 27 times units:
1%2F2=1%2Ae%5E%28k%2A27%29---simply plugged-in the values about the half life...
ln%281%2F2%29=ln%28e%5E%28k%2A27%29%29
27%2Ak%2Aln%28e%29=ln%281%2F2%29
k=%281%2F27%29ln%281%2F2%29
-
The value in decimalized form for k is highlight_green%28-0.02567%29.

Now your question is, t=what for A=0.88%2AA%5Bo%5D ?
highlight%280.88=1%2Ae%5E%28-0.02567%2At%29%29
...
..
!