An isotope has a half-life of 65 min. If the decay is modeled by the differential equation dy/dt = -ky, where t is measured in minutes, what is the decay constant k?

Can someone explain this to me? What I have to do, and why?

Greatly appreciated!

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- Nov 30th 2009, 06:26 PMMorgan82Half-life
An isotope has a half-life of 65 min. If the decay is modeled by the differential equation dy/dt = -ky, where t is measured in minutes, what is the decay constant k?

Can someone explain this to me? What I have to do, and why?

Greatly appreciated! - Nov 30th 2009, 07:00 PMfelper
$\displaystyle \frac{dy}{dt}=y'=-ky \Rightarrow \frac{y'}{y}=-k$

Then, you can integrate both sides respect to time, and use the given condition to determinate the constants.