Answer
$45.4min$
Work Step by Step
Step 1. Given $T_0=24^\circ F, C=65^\circ F, t=10min, T=30^\circ F$, we use Newton's Law of Cooling $T=C+(T_0-C)e^{kt}$; thus, we have: $30=65+(24-65)e^{10k}$
Step 2. Thus $e^{10k}=\frac{35}{41}\approx0.8537$ which gives $k=\frac{ln(0.8537)}{10}\approx-0.0158$. The model equation is then $T=65-41e^{-0.0158t}$
Step 3. Letting $T=45$, we have $65-41e^{-0.0158t}=45$ and $e^{-0.0158t}=\frac{20}{41}$; thus $t=-\frac{ln(20/41)}{0.0158}\approx45.4min$
