SOLUTION: 320 mg of Iodine 131 is stored in a laboratory for 40 days. At the end of this period only 10 mg of the element remains. What is the half-life of Iodine 131?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 320 mg of Iodine 131 is stored in a laboratory for 40 days. At the end of this period only 10 mg of the element remains. What is the half-life of Iodine 131?      Log On


   

Question 924347: 320 mg of Iodine 131 is stored in a laboratory for 40 days. At the end of this period only 10 mg of the element remains. What is the half-life of Iodine 131?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Start with a general exponential decay equation and solve for for t and for k.

A generalized exponential decay equation: y=b%2Ae%5E%28kt%29 using assigned variables,
y, amount at any time t
b, initial amount at t=0
k, a rate constant which will be negative
t, passage of time in day

SOLVE THE DECAY EQUATION SYMBOLICALLY FOR THE TERM kt:
TAKE LOGs OF BOTH SIDES, A FEW STEPS NOT SHOWN HERE BUT SHOULD STILL BE UNDERSTOOD (HOPEFULLY):
ln%28y%29=ln%28b%29%2Bln%28e%5E%28kt%29%29
ln%28y%29=ln%28b%29%2Bkt
kt=ln%28y%29-ln%28b%29
highlight_green%28kt=ln%28y%2Fb%29%29; first use this to find k from the first two sentence. Use the green outlined equation again to find half-life.