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Math Help - assistance please

  1. #1
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    assistance please

    can any 1 help me get tru this single problem ...please
    any help will be greatly accepted

    A thermometer reading 11C is brought into a room with a constant temperature of 20C. If the thermometer
    reads 18C after 3 minutes, what will it read after being in the room for 5 minutes? Assume the cooling follows
    Newton's Law of Cooling:
    U = T + (U0 - T)e^kt.
    Last edited by mr fantastic; November 16th 2010 at 08:29 PM.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Use the curve given to you to find the value of the constants.

    U = T + (U_o - T)e^{kt}

    At time t = 3, the temperature is 18 C.

    18 = 20 + (11 - 20)e^{3k}

    Find the value of k.

    Then, use the equation again with the value of k you obtained and t = 5. FInd the value of U.

    What do you get?
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  3. #3
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    e^{kt}= left(e^k\right)^t so you really only need to find e^k, not k itself.
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  4. #4
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    newton law of cooling

    needs some assistance with this question please


    A thermometer reading 11C is brought into a room with a constant temperature of 20C. If the thermometer
    reads 18C after 3 minutes, what will it read after being in the room for 5 minutes? Assume the cooling follows
    Newton's Law of Cooling:
    <br />
U = T + (U0 - T)e^{kt}<br />
    (Round your answer to two decimal places.)

    reach as far as this
    <br />
18 = 20 + (11 - 20)e^{3k}<br />
    dont no if it is correct
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  5. #5
    A Plied Mathematician
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    I think you'll find that, with the way you've written the equation, k < 0. Try to solve for k. What do you get?
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  6. #6
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    only reach as far as here





    wat to do from here
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  7. #7
    A Plied Mathematician
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    Ok. So far, so good. Now you need to "undo" the exponential function in order to get at the exponent. How do you "undo" an exponential?
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  8. #8
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    not sure how thats done
    can u break it down futher5 for me please
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  9. #9
    A Plied Mathematician
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    What is the function inverse of the exponential function? If I have the equation y=e^{x}, how could I solve for x?
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  10. #10
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    is it this

    <br />
ln (\frac{2}{9}) = ln (e)^{3k}<br />


    <br />
3k ln (e) = ln (\frac{2}{9})<br />

    <br />
3k ln (e) = ln (\frac{2}{9})<br />



    <br />
3k  = -1.5040<br />

    <br />
k  = -0.501359133<br />
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  11. #11
    A Plied Mathematician
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    Well, I would write it this way (being careful with parentheses):

    \ln\left(\dfrac{2}{9}\right)=\ln\left(e^{3k}\right  ).

    But that's definitely the right idea. Now what?
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  12. #12
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    <br />
-1.5040774  =  3kln (e)<br />
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  13. #13
    A Plied Mathematician
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    Keep going!
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  14. #14
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     <br />
-1.5040774 = 3k<br /> <br />
k = -0.501359133<br />
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  15. #15
    A Plied Mathematician
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    So, k = -0.501359133. Now what?
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