Answer
$26.4min$
Work Step by Step
Step 1. We are given:
$T_0=28^\circ F, C=75^\circ F, t=10min, T=38^\circ F$
Use Newton's Law of Cooling
$T=C+(T_0-C)e^{kt}$
We have:
$38=75+(28-75)e^{10k}$
Step 2. Thus
$e^{10k}=\frac{37}{47}\approx0.7872$
which gives
$k=\frac{ln(0.7872)}{10}\approx-0.0239$.
The model equation is then
$T=75-47e^{-0.0239t}$
Step 3. Let $T=50$; we have
$75-47e^{-0.0239t}=50$
and
$e^{-0.0239t}=\frac{25}{47}\approx0.5319$,
Thus
$t=-\frac{ln(0.5319)}{0.0239}\approx26.4min$
