A turkey with a temperature of 40°F is moved to a 350°F oven. After 4 hours the internal temperature of the turkey is 170°F. If the turkey is done when its temperature reaches 185°F, then how much longer must it cook?
how come?
we have $\displaystyle T' = -k(T - T_{amb})$ with $\displaystyle T_{amb} = 350$, $\displaystyle T(0) = 40$ and $\displaystyle T(4) = 170$
here $\displaystyle T$ is the temperature after time $\displaystyle t$ (in hours), $\displaystyle k$ is a constant, which we can find using $\displaystyle T(0)$ and $\displaystyle T(4)$ (as described in post #2 here, question 2), and $\displaystyle T_{amb}$ is the ambient or surrounding temperature, in this case, the temperature of the oven
you want to find $\displaystyle t$ when $\displaystyle T = 185$, then you can answer the question
yes, i would use k = 0.1359 though
so we have $\displaystyle T(t) = -310e^{-0.1359t} + 350$
so now we want to know how long it takes for T to become 185, so we want t such that
$\displaystyle 185 = -310e^{-0.1359t} + 350$
now solve for $\displaystyle t$. note that this gives the total time for the turkey to get to that temperature. you want the difference between 4 and that time