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# A detective finds a murder victim at 9 am. The temperature of the body is measured at $90.3^{\circ} \mathrm{F}$. One hour later, the temperature of the body is $89.0^{\circ} \mathrm{F}$. The temperature of the room has been maintained at ta constant $68^{\circ} \mathrm{F}$. Assuming the temperature, T, of the body obeys Newton's Law of Cooling, write a differential equation for T.

Solution

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Temperature of the room is $68\text{\textdegree}$F. Let $H$ be the temperature of the body.

$\begin{equation*} \dfrac{dH}{dt}=-(H-68)k \end{equation*}$

where $k$ is a positive constant.

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