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Math Help - Finding time

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    Finding time

    A turkey with a temperature of 40F is moved to a 350F oven. After 4 hours the internal temperature of the turkey is 170F. If the turkey is done when its temperature reaches 185F, then how much longer must it cook?
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    Quote Originally Posted by dc52789 View Post
    A turkey with a temperature of 40F is moved to a 350F oven. After 4 hours the internal temperature of the turkey is 170F. If the turkey is done when its temperature reaches 185F, then how much longer must it cook?
    It seems you need to know the initial internal temperature too.
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    Quote Originally Posted by dc52789 View Post
    A turkey with a temperature of 40F is moved to a 350F oven. After 4 hours the internal temperature of the turkey is 170F. If the turkey is done when its temperature reaches 185F, then how much longer must it cook?
    see here

    post #2 also includes links to 2 other posts that may help
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    Quote Originally Posted by Jhevon View Post
    see here

    post #2 also includes links to 2 other posts that may help
    Not sure if that really helps.
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    Quote Originally Posted by dc52789 View Post
    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
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    Quote Originally Posted by Jhevon View Post
    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.
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    Quote Originally Posted by dc52789 View Post
    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"
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    Quote Originally Posted by Jhevon View Post
    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
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    Quote Originally Posted by dc52789 View Post
    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
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  10. #10
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    Quote Originally Posted by Jhevon View Post
    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?
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    Quote Originally Posted by dc52789 View Post
    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
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