SOLUTION: Problem: "a type of reactive substance decays at a rate of -8.6% daily." Model: P=Poe^kt They are asking to solve the equation algebraically and I do not see how, can you explain

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Problem: "a type of reactive substance decays at a rate of -8.6% daily." Model: P=Poe^kt They are asking to solve the equation algebraically and I do not see how, can you explain       Log On


   

Question 427536: Problem: "a type of reactive substance decays at a rate of -8.6% daily." Model: P=Poe^kt
They are asking to solve the equation algebraically and I do not see how, can you explain to me, please? Thank you so much
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Problem: "a type of reactive substance decays at a rate of -8.6% daily." Model:
P = Po*e^kt
:
We can find k by solving it for 1 day,
Let Po = 100
then
P = 100 - 8.6 = 91.4
and
t = 1 day
:
100*e^(-1k) = 91.4
e^(-1k) = 91.4%2F100
e^-k = .914
Find the nat log of both side
ln(e^-k) = ln(91.4)
-k*ln(e) = ln(91.4)
ln of e is 1 so we have
-k = -.0899247
k = .0899247
:
Now the equation for this substance
A = Ao*e(-.099247t)
where
Ao = initial amt
A = resulting amt after t days