SOLUTION: Please show all work. Thanks in advance. 1. The half life of carbon14 is 5730 yrs. How long does it take for 2.8 grams of carbon 14 to be reduced to 1.1 grams ofcarbon-14 by rad

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Please show all work. Thanks in advance. 1. The half life of carbon14 is 5730 yrs. How long does it take for 2.8 grams of carbon 14 to be reduced to 1.1 grams ofcarbon-14 by rad      Log On

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Question 595563: Please show all work. Thanks in advance.
1. The half life of carbon14 is 5730 yrs. How long does it take for 2.8 grams of carbon 14 to be reduced to 1.1 grams ofcarbon-14 by radioactive decay? (Don't round to the final answer.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The half life of carbon14 is 5730 yrs.
How long does it take for 2.8 grams of carbon 14 to be reduced to 1.1 grams ofcarbon-14 by radioactive decay?
(Don't round to the final answer.)
:
The radioactive decay formula: A = Ao*2^(-t/h), where
A = resulting amt after t time
Ao = initial amt
t = decay time
h = half-life of substance
:
2.8*2^(-t/5730) = 1.1
Divide both sides by 2.8
2^(-t/5730) = 1.1%2F2.8
2^(-t/5730) = .392857
Using nat logs
ln[2^(-t/5730)] = ln(.392857)
log equiv of exponents
-t%2F5730*ln(2) = ln(.392857)
-t%2F5730 = ln%28.392857%29%2Fln%282%29
find the ln
-t%2F5730 = -1.3479
Multiply both sides by -5730
t = -1.3479 * -5730
t = 7,723.6 yrs to decay to 1.1 grams