SOLUTION: The radioactive isotope you discovered at 8 am weighed 75 mg. At 3 pm it measured only 0.009 grams. Rounded to the nearest whole minute, what is its half life?

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: The radioactive isotope you discovered at 8 am weighed 75 mg. At 3 pm it measured only 0.009 grams. Rounded to the nearest whole minute, what is its half life?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 857775: The radioactive isotope you discovered at 8 am weighed 75 mg. At 3 pm it measured only 0.009 grams. Rounded to the nearest whole minute, what is its half life?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A=Ie%5E%28-kt%29, I is initial amount, A is final amount after time t.

FIND k
ln%28A%29=ln%28I%29-kt
-kt=ln%28A%29-ln%28I%29
k=%281%2Ft%29%28ln%28I%29-ln%28A%29%29
k=%281%2Ft%29ln%28I%2FA%29
k=%281%2F7%29ln%2875%2F0.009%29
highlight%28k=1.29%29

USE k TO FIND HALF-LIFE
Decay equation is highlight_green%28A=Ie%5E%28-1.29t%29%29.
Let A=1/2 and let I=1.
Solve for t.