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Thread: Find the constants a and b of the function V=aP^b, given table of values

  1. #1
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    Find the constants a and b of the function V=aP^b, given table of values

    I need to find the constants a and b of the function V=aP^b
    I have a table of values of P and V but I am not sure how to proceed
    Thanks in advance

  2. #2
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    Quote Originally Posted by Elson View Post
    I need to find the constants a and b of the function V=aP^b
    I have a table of values of P and V but I am not sure how to proceed
    Thanks in advance
    Take "log" of the equation and plot the tabulated values.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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    Please could you explain further?
    I have included the table of values if that helps
    Thanks

    P 126 178 263 398 525 724
    V 1.86 2.34 2.75 3.63 4.17 4.79

  4. #4
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by Elson View Post
    Please could you explain further?
    I have included the table of values if that helps
    Thanks

    P 126 178 263 398 525 724
    V 1.86 2.34 2.75 3.63 4.17 4.79
    Are you not familiar with logarithms? If not, then what method has your class covered for this sort of exercise? Are you supposed to do a regression in your graphing calculator? If so, then where are you getting stuck?

    Please be complete. Thank you!

  5. #5
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    If this is not for a math class, and you just need an answer, you can put the data into an Excel spreadsheet and make a scatterplot, then create a trendline, specifying "power", and ask it to show the equation. This will do the regression for you. If it is for a class, you need to state the instructions.

    It would be very helpful if you told us the context of the question, so we would know what kind of help you need.

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    The full question is the fore P newtons required to keep an object moving at a speed V meters per second was recorded.
    P 126 178 263 398 525 724
    V 1.86 2.34 2.75 3.63 4.17 4.79
    The law connecting P and is of the form V = aP^b where a and b are constants. Use appropriate graphical and algebraic techniques to find the values of a and b.
    I am familiar with logs but I am not sure how to use them to find a and b
    Thanks

  7. #7
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    Quote Originally Posted by Elson View Post
    The full question is the fore P newtons required to keep an object moving at a speed V meters per second was recorded.
    P 126 178 263 398 525 724
    V 1.86 2.34 2.75 3.63 4.17 4.79
    The law connecting P and is of the form V = aP^b where a and b are constants. Use appropriate graphical and algebraic techniques to find the values of a and b.
    I am familiar with logs but I am not sure how to use them to find a and b
    Thanks
    [tex]\text {Let } v = log(V) \text { and } p = log(P) \text { and } c = log(a).[/tex]

    [tex]\therefore V = aP^b \implies log(V) = log(aP^b) \implies v = log(a) + b * log(P) = c + bp.[/tex]

    But v = c + bp is a linear equation. You can compute the values of v and p, use linear regression to find estimates of c and b, and convert c to a how?

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