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A radioactive substance decays according to the following function, where yo is the initial amount present, and y is the amount present at time t (in days).-0.0415ty=yoeFind the half-life of this substance. Do not round any intermediate computations, and round your answer to the nearest tenth.daysX5 ?

A radioactive substance decays according to the following function where yo is the initial amount present and y is the amount present at time t in days00415tyyo class=

Respuesta :

we have the equation

[tex]y=y_0e^{-0.0415t}[/tex]

Half-time is the time when y=y0/2

substitute

[tex]\begin{gathered} \frac{y_0}{2}=y_0e^{-0.0415t} \\ \\ simplify \\ \frac{1}{2}=e^{-0.0415t} \end{gathered}[/tex]

Solve for t

Apply ln on both sides

[tex]\begin{gathered} ln(\frac{1}{2})=ln(e^{-0.0415t}) \\ \\ ln(\frac{1}{2})=-0.0415t \\ t=\frac{ln(\frac{1}{2})}{-0.0415} \\ \\ t=16.7\text{ days} \\ \end{gathered}[/tex]