SOLUTION: A particular radioactive isotope decays from 220 milligrams (mg) to 184.8 mg in 17 days. Find the half life of the isotope. Your answer is ___ days.

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Question 729751: A particular radioactive isotope decays from 220 milligrams (mg) to 184.8 mg in 17 days. Find the half life of the isotope.
Your answer is ___ days.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
General form, A%28t%29=I%2Ae%5E%28-k%2At%29, I means initial amount, A(t) is amount at time t.

184.8=220%2Ae%5E%28-k%2A17%29
%28184.8%2F220%29=e%5E%28-k%2A17%29
0.84=e%5E%28-k%2A17%29
ln%280.84%29=-k%2A17%2Aln%28e%29
-%281%2F17%29%2Aln%280.84%29=k
highlight%28k=0.01026%29

The specific model equation is highlight%28A%28t%29=I%2Ae%5E%28-0.01026%2At%29%29. Half Life is found through 1%2F2=1%2Ae%5E%28-0.01026%2At%29, and you want to find t.