SOLUTION: A tumor is injected with 0.6 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 ->  Exponential-and-logarithmic-functions -> SOLUTION: A tumor is injected with 0.6 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


   



Question 1156567: A tumor is injected with 0.6 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 ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
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The decay equation in this case is


    M = M%5B0%5D%2A%281-0.0115%29%5Et = M%5B0%5D%2A0.9885%5Et,


where M%5B0%5D is the original mass, M is the current mass, t is the time in days.


They want you find "t"  from the condition  M = 0.5%2AM%5B0%5D.


It gives


    0.5 = 0.9885%5Et.


Take the logarithm base 10 from both sides


    log(0.5) = t*log(0.9885).


Hence,  t = log%28%280.5%29%29%2Flog%28%280.9885%29%29 = 59.93 = 60 days  (rounded as required).    ANSWER

Solved.