## Related questions with answers

Coroners estimate the time of death using the rule of thumb that a body cools about $2^{\circ} \mathrm{F}$ during the first hour after death and about $1^{\circ} \mathrm{F}$ for each additional hour. Assuming an air temperature of $68^{\circ} \mathrm{F}$ and a living body temperature of $98.6^{\circ} \mathrm{F}$, the temperature $T(t)$ in ${ }^{\circ} \mathrm{F}$ of a body at a time $t$ hours since death is given by

$T(t)=68+30.6 e^{-k t} .$

$\bull$ Using the value of $k$ found in part (a), show that, 24 hours after death, the coroner's rule of thumb gives approximately the same temperature as the formula.

Solution

VerifiedThe problem asks to show that the coroner's rule of thumb is almost the same as the given function for the temperature of the body.

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