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Math Help - Graphs and equations of straight line

  1. #1
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    Graphs and equations of straight line

    The variable x and y are connected by the law y=Ce^ax,where a,C and e are constant.The experimental values of x and y are recorded in the following table

    x 1 2 3 4
    y 6.59 10.87 17.90 29.56


    plot a graph of log y against x.Given that log e=0.4343,use graph to find the values of a and c..

    please shows steps by step the answer that you get..thanks!!!..
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    The variable x and y are connected by the law y=Ce^ax,where a,C and e are constant.The experimental values of x and y are recorded in the following table

    x 1 2 3 4
    y 6.59 10.87 17.90 29.56


    plot a graph of log y against x.Given that log e=0.4343,use graph to find the values of a and c..

    please shows steps by step the answer that you get..thanks!!!..
    The first step is to take the logarithm of y and plot those points. If y= Ce^{ax} then log(y)= log(C)+ a log(e)x, a straight line with slope a log(e) and y-intercept log(C). (The logarithm here is the common logarithm, base 10, since they tell you that log(e)= 0.4343)
    The y value, where the line crosses the y-axis, is log(C) and so C= 10^y for that y value. a is the slope of that line divided by log(e)= 0.4343. If this were exactly a straight line, you could calculate the slope using any two points but with inexact measurements, it is best to use the two points farthest apart: the slope would be \frac{log(29.56)- log(6.59)}{4- 1}.
    Last edited by HallsofIvy; February 3rd 2010 at 07:58 AM.
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    Quote Originally Posted by HallsofIvy View Post
    The first step is to take the logarithm of y and plot those points. If y= Ce^{ax} then log(y)= log(C)+ a log(e)x, a straight line with slope a log(e) and y-intercept log(C). (The logarithm here is the common logarithm, base 10, since they tell you that log(e)= 0.4343)
    The y value, where the line crosses the y-axis, is log(C) and so C= 10^y for that y value. a is the slope of that line divided by log(e)= 0.4343. If this were exactly a straight line, you could calculate the slope using any two points but with inexact measurements, it is best to use the two points farthest apart: the slope would be \frac{log(29.56)- log(6.59)/(4- 1).

    i get the value of c but i dont get a value of a..can u help me?the value of c i get 4.0
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  4. #4
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    Sorry, I messed up the LaTex exactly where I was addressing that point. The slope of the line is log(29.56)- log(6.59)}{4- 1} and a is that number divided by 0.4343.
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