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Working out an equation

  1. Nov 27, 2009 #1
    Hello!
    Theres a relationship in which the temperature decreases with time:
    It starts at 100 degrees C, then decreases by 10, then 9, then 8, then 7 and so on per minute. Is it possible to come up with a function for this? I tried working back from the second derivitive, which is +1, then integrated it with respect to time:
    [tex]\int{1} dx = x + c[/tex]
    I figured since it starts by removing 10 from 100, then c = -10.
    I then took the integral of this:
    [tex]\int{x - 10) dx = \frac{x^2}{2} - 10x + c[/tex]
    Can I get this to fit what I need? It goes wrong from here as I don't think this fits what I need.
    Thanks in advance.
     
  2. jcsd
  3. Nov 27, 2009 #2
    Just because it starts decreasing by ten, doesn't mean it always decreases by ten.

    Integrating:
    f''(x) = 1
    f'(x) = x + c
    f(x) = x2/2 + cx + d

    And you have that f(0) = 100 and f(1) = 90, so use those to find c and d (or use any two initial conditions that you want).

    I tested some values in the final equation that I got:

    x - f(x)
    0 - 100
    1 - 90
    2 - 81
    3 - 73
    4 - 66
     
  4. Nov 27, 2009 #3
    Thanks pbandjay.
     
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