Answer
a. $T=45+25e^{-0.0916t}$
b. $51.3^\circ F$
c. $17.6min$
Work Step by Step
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 $t=-\frac{ln(0.2)}{0.0916}\approx17.6min$
