SOLUTION: Suppose a sample of a radioactive substance weighs 30 mg. One year later, the sample weighs 27.5 mg. What is the half-life of this substance? (Round your answer to two decimal plac

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Suppose a sample of a radioactive substance weighs 30 mg. One year later, the sample weighs 27.5 mg. What is the half-life of this substance? (Round your answer to two decimal plac      Log On


   

Question 1153051: Suppose a sample of a radioactive substance weighs 30 mg. One year later, the sample weighs 27.5 mg. What is the half-life of this substance? (Round your answer to two decimal places.)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
27.5=30%2Ab%5E1
b=27.5%2F30
b=0.9166667, approximation


y=p%2Ab%5Ex
y=p%280.9166667%29%5Ex
1%2A%280.9166667%29%5Ex=%281%2F2%29
log%28%280.9166667%29%5Ex=log%28%281%2F2%29%29
x%2Alog%28%280.9166667%29%29=log%28%281%2F2%29%29
highlight%28x=log%28%281%2F2%29%29%2Flog%28%280.9166667%29%29%29

half-life, 7.97 years

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the half-life in years. Then 1 year is (1/x) half-lives.

30%28.5%29%5E%281%2Fx%29+=+27.5
.5%5E%281%2Fx%29+=+11%2F12
%281%2Fx%29log%28.5%29+=+log%2811%2F12%29
x+=+log%28.5%29%2Flog%2811%2F12%29+=+7.97 to 2 decimal places