Question

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

Answer 1

The half-life 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 half-life.

Answer 2

so the half life is 8 ln 2 years?

Answer 3

Yes. About 5.5yrs.

Answer 4

thanks again