SOLUTION: Suppose a radioactive isotope is such that five-sixths of the atoms in a sample decay after nine days. Find the half-life of this isotope. Round your answer to 2 decimal places.

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Question 515381: Suppose a radioactive isotope is such that five-sixths of the atoms in a sample decay after nine days. Find the half-life of this isotope.
Round your answer to 2 decimal places.
______ days.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Suppose a radioactive isotope is such that five-sixths of the atoms in a sample decay after nine days.
Find the half-life of this isotope.
:
the radioactive decay formula: A = Ao*2^(-t/h), where
A = Amt remaining after t time
Ao = Initial Amt
t = time
h = half-life of substance
:
Let initial amt = 1
1*2^(-9/h) = 5%2F6
Use natural logs
ln(2^(-9/h)) = ln(5/6)
The log equiv of exponents
-9%2Fh*ln(2) = ln(5/6)
-9%2Fh = ln%285%2F6%29%2Fln%282%29
using a calc
-9%2Fh = -.263
-.263h = -9
h = %28-9%29%2F%28-.263%29
h = 34.2 days, half-life of substance