Answer
a. $T=72+303e^{-0.0769t}$
b. $6.9\ min$
Work Step by Step
Using the given equation
$T=C+(T_0-C)e^{kt}$
with the conditions
$T_0=375^\circ F, C=72^\circ F$
we have:
a. For $t=60\ min, T=75^\circ F$, we have
$75=72+(375-72)e^{60k}$
or
$303e^{60k}=3$, thus $k=\frac{ln(3/303)}{60}\approx-0.0769$
and the model equation is
$T=72+303e^{-0.0769t}$
b. Letting $T=250^\circ F$, we have
$250=72+303e^{-0.0769t}$
and
$t=-\frac{ln(178/303)}{0.0769}\approx6.9\ min$
