## Precalculus (6th Edition) Blitzer

a. $T=45+25e^{-0.0916t}$ b. $51.3^\circ F$ c. $17.6min$
Using Newton's Law of Cooling $T=C+(T_0-C)e^{kt}$, we have: a. We have: $T_0=70^\circ F, C=45^\circ F, t=10min, T=55^\circ F$ Thus $55=45+(70-45)e^{10k}$ and $e^{10k}=\frac{10}{25}=0.4$ This gives $k=\frac{ln(0,4)}{10}\approx-0.0916$ The model equation is then $T=45+25e^{-0.0916t}$ b. With $t=15min$, we have $T=45+25e^{-0.0916(15)}\approx51.3^\circ F$ c. Letting $T=50$, we have $45+25e^{-0.0916t}=50$ and $e^{-0.0916t}=\frac{5}{25}=0.2$ Thus $t=-\frac{ln(0.2)}{0.0916}\approx17.6min$