SOLUTION: The half-life of a particular radioactive isotope is 72 hours. Write an equation to relate the mass of radioactive material remaining to time (in hours). Starting with 170g,

Algebra ->  Exponents -> SOLUTION: The half-life of a particular radioactive isotope is 72 hours. Write an equation to relate the mass of radioactive material remaining to time (in hours). Starting with 170g,       Log On


   

Question 1113943: The half-life of a particular radioactive isotope is 72 hours.
Write an equation to relate the mass of radioactive material remaining to time (in hours).
Starting with 170g, what mass will remain in 3 weeks?
If after one day (24 hours), a different sample of the material was found to have a mass of 14 mg with a half-life of 12h, what was the initial mass of the sample?
solve using log if possible
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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The half-life of a particular radioactive isotope is 72 hours.
Write an equation to relate the mass of radioactive material remaining to time (in hours).
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y=pe%5E%28-kt%29
ln%28y%29=ln%28p%29%2Bln%28e%5E%28-kt%29%29
ln%28y%29=ln%28p%29-kt
ln%28y%29-ln%28p%29=-kt
kt=ln%28p%29-ln%28y%29

k=%281%2Ft%29%28ln%28p%2Fy%29%29

If half life is 72 hours, then k=%281%2F72%29%2Aln%282%29
k=0.009627

This model then becomes highlight%28y=p%2Ae%5E%28-0.009627t%29%29
p, initial quantity
y, final quantity
t, time in hours

You can figure the other questions based on that.