SOLUTION: Suppose a sample of a radioactive substance weighs 38 mg. One year later, the sample weighs 21.5 mg. What is the half-life of this substance? (Round your answer to two decimal plac

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Suppose a sample of a radioactive substance weighs 38 mg. One year later, the sample weighs 21.5 mg. What is the half-life of this substance? (Round your answer to two decimal plac      Log On


   

Question 1057609: Suppose a sample of a radioactive substance weighs 38 mg. One year later, the sample weighs 21.5 mg. What is the half-life of this substance? (Round your answer to two decimal places.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Suppose a sample of a radioactive substance weighs 38 mg.
One year later, the sample weighs 21.5 mg.
What is the half-life of this substance? (Round your answer to two decimal places.)
:
Use the radioactive decay formula: A = Ao*2^(-t/h), where:
A = Amt of remaining after t time
Ao = Initial amt
t = time of decay
h = half-life of the substance
in this problem
A = 21.5
Ao = 38
t = 1 year
h = half life of substance
:
38%2A2%5E%28-1%2Fh%29+=+21.5
2%5E%28-1%2Fh%29+=+21.5%2F38
2%5E%28-1%2Fh%29+=+.5658
using Natural logs
%28-1%2Fh%29ln%282%29+=+ln%28.5658%29
%28-1%2Fh%29%2A.6931+=+-.5695%29
-1%2Fh+=+%28-.5695%29%2F.6931%29
-1%2Fh+=+-.8216
h = %28-1%29%2F%28-.8216%29
h = 1.22 yrs is the half life
:
:
Check this with a calc enter: 38*2^(-1/1.22) ~ 21.5