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Math Help - Instantaneous Rate of Change

  1. #1
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    Instantaneous Rate of Change

    Can someone help me solve this problem... I need to calculate the instantaneous rate of change for the following points:


    1. 1985
    2. 1995
    3. 2000
    4. 2006

    -------------

    Based on this data:


    Year Public Sector Employment (Number of People in Millions)

    1981 2.69009
    1982 2.72483
    1983 2.74130
    1984 2.76072
    1985 2.79665
    1986 2.84086
    1987 2.87816
    1988 2.94450
    1989 2.96726
    1990 3.02734
    1991 3.05678
    1992 3.06323
    1993 3.03748
    1994 3.00269
    1995 2.95784
    1996 2.85133
    1997 2.78940
    1998 2.77897
    1999 2.76987
    2000 2.78673
    2001 2.81360
    2002 2.84346
    2003 2.90811
    2004 2.94086
    2005 2.97973
    2006 3.04614


    The equation I got for this was y = 0.0002x^3 - 1.3853x^2 + 2763.2x - 2000000


    Can you please just help me with the first one... After i understand how to do the first oen I'll know how to do the rest.

    Thanks
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  2. #2
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    You have

     y = 0.0002x^3 - 1.3853x^2 + 2763.2x - 2000000

    find \frac{dy}{dx} and sub in your points.
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  3. #3
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    Quote Originally Posted by pickslides View Post
    You have

     y = 0.0002x^3 - 1.3853x^2 + 2763.2x - 2000000

    find \frac{dy}{dx} and sub in your points.
    I can't use calculus ... I have to do it algebraically I think... I tried this out but for some reason I get 1 786 499 600 which has to be wrong... I did the calculations twice though and its the same answer...

    I really need help for this... I tried it again and I get 1 390 827.59 - 1 296 690.71 for my final answer... but that still is an error for a question like this.... I think i messed up somewhere in the calculations but i'm not sure where.
    Last edited by mr fantastic; January 15th 2010 at 03:47 AM.
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  4. #4
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    Quote Originally Posted by agent2421 View Post
    I need to calculate the instantaneous rate of change
    This implies the use of calculus
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  5. #5
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    yes but we can also calculate it algebraically... I have not learned calculus yet so I can't use calculus...


    We have an equation and then we use the formula:

    m = f (x+h) - f (x) / (x+h) - x

    = f (x+h) - f (x) / h


    I used this formula but I can't get it right...
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  6. #6
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    Quote Originally Posted by agent2421 View Post

    = f (x+h) - f (x) / h
    Ok then, show me your workings.
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  7. #7
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    m = 0.002 (1985 + 0.0001)^3 - 1.3853 (1985 + 0.0001)^2 + 2763.2 (1985 + 0.0001) - 2 000 000 - [0.002 (1985)^3 - 1.3853 (1985)^2 + 2673.2 (1985) - 2000000]

    = 13699253.6 - 13494541.7

    = 204711.6/.0001

    = 2 047 117 000


    That can't be the answer since I"m looking for instantaneous rate of change... I'm going wrong somewhere but I have no idea where... Can someone please help me for this.
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  8. #8
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    Why did you pick h = 0.0001 ?
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  9. #9
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    There's an example of the same type of question in my book and it used h = .0001... they were trying to find the instantaneous rate of change for 2006....

    I just followed the same example and used .0001
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