Chapter 4.2, Problem 69PE

(a)

To determine

A function that models the temperature $T(t)$ (in °F) of the cake t minutes after being removed from the oven, if The equation $T\left(t\right)=T_a+\left(T_0-T_a\right)e^{-kt}$, where $T_a$ represents the surrounding temperature, $T_o$ represents the initial temperature of the object, and t is the time after the object starts cooling. k is the cooling rate. Also $T_a=78°\text{F}$, $T_0=350°\text{F}$, and $k=0.046$

(b)

To determine

The temperature of the cake $10\min$ after coming out of the oven for the equation is $T\left(t\right)=78+272e^{-0.046t}$.

(c)

To determine

If Jessica waits an hour to frost the cake, will the cake be cool enough to frost for the equation $T\left(t\right)=78+272e^{-0.046t}$.