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anonymous
 5 years ago
suppose the amount of radioactive substance left after t years is given by
A(t)=50e^(0.0125t).Find the half life of this radioactive substance
anonymous
 5 years ago
suppose the amount of radioactive substance left after t years is given by A(t)=50e^(0.0125t).Find the half life of this radioactive substance

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The halflife is defined to be the amount of time needed for half the original amount to decay. The original amount is found when t = 0 (i.e. from when we start measuring). At t=0, A(0)=50...so this is your initial amount. At time t = u, half of the original amount will have decayed. So you'd have at this time, 25=50e^(0.0125u) > 1/2=e^(0.0125u) Take the natural log of both sides:\[\ln 1/2 = \ln (e^{0.0125u}) \rightarrow \ln 2 = 0.0125u \rightarrow u = \frac{\ln 2}{0.0125}\]i.e.\[u=8 \ln 2\]years. This is your halflife.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the half life is 8 ln 2 years?
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