SOLUTION: A tumor is injected with 0.2 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A tumor is injected with 0.2 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?       Log On

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Question 1139498: A tumor is injected with 0.2 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The given information -- a decay rate of 1.15% per day -- means that each day the amount remaining at the end of the day is 100-1.15 = 98.85% of the amount at the beginning of the day. So after t days the fraction of the original amount remaining is

%280.9885%29%5Et

You want to know the number of days t it takes for the remaining amount to be half the original amount:

0.9885%5Et+=+0.5

The variable is in the exponent, so you need to use logarithms (or a graphing calculator, or some similar mathematical aid).

t%2Alog%28%280.9885%29%29+=+log%28%280.5%29%29
t+=+log%28%280.5%29%29%2Flog%28%280.9885%29%29+=+59.92 to 2 decimal places.

ANSWER: to the nearest day, it will take 60 days for half of the iodine-125 to decay.