Question 1014988: Please help me answer this word problem:
The rate at which a radioactive isotope disintegrates is proportional to the amount present. If a 30g sample will contain only 20g after ten minutes, what is the half-life of this isotope, correct to the nearest tenth of a minute? Answer this question by first finding the amount y of this isotope as a function of time t(in minutes) in the form y=y0e^kt.
Thank-you, your help is always appreciated!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! y=yoe^kt
20=30e^10k
(2/3)=e^10k
ln of both sides, then divide by 10 without rounding.
ln(2/3)=10k
k=-0.04055
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Now for half life
y=(1/2)yo, so
(1/2)=e^(-0.04055)t
ln of both sides, then divide by coefficient of t
-0.693/-0.04055
t=17.09 minutes. This makes intuitive sense, since 10 minutes is not the half life but is getting close to it.
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