## Precalculus (6th Edition) Blitzer

$26.4min$
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 $t=-\frac{ln(0.5319)}{0.0239}\approx26.4min$