SOLUTION: A substance decays exponentially. If the 80 ounces of the substance decays to 9 ounces in 3 hours. What is the half - life of the substance?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A substance decays exponentially. If the 80 ounces of the substance decays to 9 ounces in 3 hours. What is the half - life of the substance?      Log On


   

Question 892641: A substance decays exponentially. If the 80 ounces of the substance decays to 9 ounces in 3 hours. What is the half - life of the substance?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
p=Ie%5E%28-kt%29, generalized exponential decay equation
p, how much present at time t starting from initial amount I
I, initial amount when t=0
t, time
k, a constant
e, the Euler number, base of Natural logarithm

First, find k using I=80, p=9, t=3.
ln%28p%29=ln%28Ie%5E%28-kt%29%29
ln%28I%29%2Bln%28e%5E%28-kt%29%29=ln%28p%29
ln%28I%29%2B%28-k%29t%2A1=ln%28p%29
-kt=ln%28p%29-ln%28I%29
k=-%281%2Ft%29%28ln%28p%29-ln%28I%29%29
highlight%28k=-%281%2Ft%29%28ln%28p%2FI%29%29%29
For the value of k:
k=-%281%2F3%29%28ln%289%2F80%29%29
highlight%28k=0.728%29, using k as a positive value.

Half-Life
Here, p=I%2F2.
p=I%2F2=Ie%5E%28-0.728%2At%29
1%2F2=e%5E%28-0.728t%29
ln%281%2F2%29=-0.728t%2A1
t=-1%2F%280.728%29ln%281%2F2%29
highlight%28t=0.952%29 in hours.