Question

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 ?

Answer 1

we have the equation

`y=y_0e^(-0.0415t)`

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

substitute

`\begin{gathered} (y_0)/(2)=y_0e^(-0.0415t) \\ \\ simplify \\ (1)/(2)=e^(-0.0415t) \end{gathered}`

Solve for t

Apply ln on both sides

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