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Math Help - exponential/compounded growth/decay

  1. #1
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    exponential/compounded growth/decay

    So confusing,
    So I seem to be having a lot of trouble with putting compounded growth/decay related problems into context with the formulas.
    The problem is:
    A pie is removed from a 375 degree Fahrenheit oven and cools to 215 degrees. after 15 minutes in a room at 72 degrees fahrenheit. How long from the time it is removed from the oven will it take the pie to cool to 120 degrees fahrenheit?
    Im really not sure where to start but here goes
    A = P(1+r/k)^kt
    120 = 375(1+15/160)^(160t) now just use log to solve???
    did i set this up correctly?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Sxon View Post
    So confusing,
    So I seem to be having a lot of trouble with putting compounded growth/decay related problems into context with the formulas.
    The problem is:
    A pie is removed from a 375 degree Fahrenheit oven and cools to 215 degrees. after 15 minutes in a room at 72 degrees fahrenheit. How long from the time it is removed from the oven will it take the pie to cool to 120 degrees fahrenheit?
    Im really not sure where to start but here goes
    A = P(1+r/k)^kt
    120 = 375(1+15/160)^(160t) now just use log to solve???
    did i set this up correctly?
    Use Newton's Law of Cooling:

    \frac{dT}{dt}  = -kT

    which when integrated gives:

    T = T_{0}e^{-kt} where T is final temperature, T_{0} is initial temperature, k is a constant and t is time

    Plug in what you know:
    <br />
215 = 375e^(-15k)

    <br />
k = -\frac{1}{15}ln{\frac{215}{375}}

    Now we know k we can use it to find t:

    t = -\frac{1}{k}ln({\frac{T}{T_{0}})} = -\frac{1}{\frac{1}{15}ln{\frac{215}{375}}}ln({\frac  {120}{375})}
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    Use Newton's Law of Cooling:

    \frac{dT}{dt}  = -kT

    which when integrated gives:

    T = T_{0}e^{-kt} where T is final temperature, T_{0} is initial temperature, k is a constant and t is time

    Plug in what you know:
    <br />
215 = 375e^(-15k)

    <br />
k = -\frac{1}{15}ln{\frac{215}{375}}

    Now we know k we can use it to find t:

    t = -\frac{1}{k}ln({\frac{T}{T_{0}})} = -\frac{1}{\frac{1}{15}ln{\frac{215}{375}}}ln({\frac  {120}{375})}
    I came up with a negative number, and the answer is in minutes?? i'm confused, how can this be the answer?
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Sxon View Post
    I came up with a negative number, and the answer is in minutes?? i'm confused, how can this be the answer?
    Ah right, I forgot about the sign on k in the final equation. That front minus sign needn't be there[/color]
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