SOLUTION: Radioactive iodine treatment is so successful at treating hyperthyroidism that it has virtually replaced thyroid surgery. To the nearest full day, determine how long it will take f

Question 277610: Radioactive iodine treatment is so successful at treating hyperthyroidism that it has virtually replaced thyroid surgery. To the nearest full day, determine how long it will take for 400 millicuries of I-131, which has a half-life of 8 days, to decay to 3.125 millicuries.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Radioactive iodine treatment is so successful at treating hyperthyroidism that it has virtually replaced thyroid surgery.
To the nearest full day, determine how long it will take for 400 millicuries of I-131, which has a half-life of 8 days, to decay to 3.125 millicuries.
:
The half-life equation
A = Ao*2^(-t/h)
where
A = resulting amt after t days
Ao = initial amt (t=0)
t = time in days in this case
h = half-life of substance
:
400*2^(-t/8) = 3.125
:
Divide both sides by 400
2^(-t/8) = .0078125
:
log(2^(-t/8)) = log(.0078125)
which is
*log(2) = log(.0078125)
=
using a calc
= -7
t = -7 * -8
t = 56 days
;
:
Check on a calc: enter: 400*2^(-56/8) = 3.125, confirms our solution
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