Question 1088854: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced to a mass of 1 mg.
What was the initial mass (in mg) of the sample?
What is the mass 5 weeks after the start?
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! The formula for exponential decay is P=P(0)e^-kt, where P(0) is the initial population, P is the final population, k is the constant rate of decay, and t is time. Then, in this case:
P/P(0)=.5=e^-4k
ln 0.5=ln e^-4k
-0.69314718055994530941723212145818=-4k
k=0.17328679513998632735430803036454
Then, to solve for 1 mg, we hve
1=P(0)e^-0.173286795(20)
1=P(0).03125
P(0)=32
..........
5 weeks population:
P=32*e^-0.17328679513998632735430803036454(35)
P=0.07432544468767 gms
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