1. ## Finding time

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?

2. Originally Posted by dc52789
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?
It seems you need to know the initial internal temperature too.

3. Originally Posted by dc52789
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?
see here

post #2 also includes links to 2 other posts that may help

4. Originally Posted by Jhevon
see here

post #2 also includes links to 2 other posts that may help
Not sure if that really helps.

5. Originally Posted by dc52789
Not sure if that really helps.
how come?

we have $T' = -k(T - T_{amb})$ with $T_{amb} = 350$, $T(0) = 40$ and $T(4) = 170$

here $T$ is the temperature after time $t$ (in hours), $k$ is a constant, which we can find using $T(0)$ and $T(4)$ (as described in post #2 here, question 2), and $T_{amb}$ is the ambient or surrounding temperature, in this case, the temperature of the oven

you want to find $t$ when $T = 185$, then you can answer the question

6. Originally Posted by Jhevon
how come?

we have $T' = -k(T - T_{amb})$ with $T_{amb} = 350$, $T(0) = 40$ and $T(4) = 170$

here $T$ is the temperature after time $t$ (in hours), $k$ is a constant, which we can find using $T(0)$ and $T(4)$ (as described in post #2 here, question 2), and $T_{amb}$ is the ambient or surrounding temperature, in this case, the temperature of the oven

you want to find $t$ when $T = 185$, then you can answer the question
I still kinda don't get it.

7. Originally Posted by dc52789
I still kinda don't get it.
just try to work through the process as described in the last link i gave. tell me what is confusing you specifically. it's hard to help if you just say "i don't get it"

8. Originally Posted by Jhevon
just try to work through the process as described in the last link i gave. tell me what is confusing you specifically. it's hard to help if you just say "i don't get it"
o k
I have A = -310 and k = 0.136

9. Originally Posted by dc52789
o k
I have A = -310 and k = 0.136
yes, i would use k = 0.1359 though

so we have $T(t) = -310e^{-0.1359t} + 350$

so now we want to know how long it takes for T to become 185, so we want t such that

$185 = -310e^{-0.1359t} + 350$

now solve for $t$. note that this gives the total time for the turkey to get to that temperature. you want the difference between 4 and that time

10. Originally Posted by Jhevon
yes, i would use k = 0.1359 though

so we have $T(t) = -310e^{-0.1359t} + 350$

so now we want to know how long it takes for T to become 185, so we want t such that

$185 = -310e^{-0.1359t} + 350$

now solve for $t$. note that this gives the total time for the turkey to get to that temperature. you want the difference between 4 and that time
So, is the answer around 4.64?

11. Originally Posted by dc52789
So, is the answer around 4.64?
yes, that is the total time. but remember, it was already in the oven for 4 hours. so we need to tell them the excess time to get to 185