Iodine-131 is a radioactive form of iodine. After the crisis at a Japanese nuclear power plant in March 2011, elevated levels of this substance were detected thousands of miles away from Japan. Iodine-131 has a half-life of 8 days. What is the daily decay factor for this substance? (Round your answer to two decimal places.) _______

idenny
Mar 14, 2017

#2**0 **

Call A the original amount of the substance....and we have this equation

.5A = Ae^(-k*t) where k is the decay factor and t is the time in days = 8

........divide both sides by A

.5 = e^(-k*8) take the ln of both sides

ln (.5) = ln e^(-k*8) and we can write

ln (.5) =( -k*8) and ln e = 1 so we can ignore this

ln(.5) = -k * 8 divide both sides by -8

-ln(.5) / 8 = k ≈ 0.09 [rounded ]

CPhill
Mar 14, 2017