SOLUTION: How do you do this decay problem? The radioactive isotope 123I, used in nuclear imaging, decays continuously at a rate of 5.25% per hour. (a) Approximate the percentage remaini

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do you do this decay problem? The radioactive isotope 123I, used in nuclear imaging, decays continuously at a rate of 5.25% per hour. (a) Approximate the percentage remaini      Log On


   

Question 973066: How do you do this decay problem?
The radioactive isotope 123I, used in nuclear imaging, decays continuously at a rate of 5.25% per hour.
(a) Approximate the percentage remaining of any initial amount after 26.4 hours.
(b) What is the half-life of 123I?
For part a I think the formula for that is A(t)=A*e^(kt). The problem that I'm having with this is that I don't know the initial amount (A). Here are the variables:
A=?
k=?
t=26.4
It seems like it's asking what (k) would be but I don't know how to solve for (k) without knowing the initial amount (A). I think I may be looking at it wrong. Any help on this one would be appreciated. I know how to do part b but I need to know how to do part a first before I can do b.
Thank you!!


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Retention is 100-5.25=94.75 percent each hour.

Starting with quantity 1, Using the model,
0.9475=1%2Ae%5E%28k%2A1%29
0.9475=e%5Ek
ln%280.9475%29=k%2A1
highlight%28k=ln%280.9475%29%29 and the model is more specifically highlight_green%28A%28t%29=A%2Ae%5E%28-0.05393t%29%29.


HALF-LIFE
%281%2F2%29=1%2Ae%5E%28-0.05393t%29

ln%281%2F2%29=-0.05393%2At%2Aln%28e%29

t=ln%281%2F2%29%2F%28-0.05393%29

highlight%28t=12.9%29 hours