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Math Help - Gradient/intercept!

  1. #1
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    Gradient/intercept!

    ...........................
    Last edited by jisaac; June 24th 2008 at 03:10 AM.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by jisaac View Post
    The graph of radioactive count rate N against elapsed time t is an exponential; the equation of this graph is

    where N0 and λ are positive constants.

    A graph of ln N against t will be a straight line of gradient (something) and intercept of (something) on the vertical axis.

    what is the gradient and intercept?
    \begin{aligned}<br />
\ln N&=\ln\left(N_0 \mathrm{e}^{-\lambda t}\right)\\<br />
&=\ln N_0 + \ln \left( \mathrm{e}^{-\lambda t}\right)\\<br />
&=\ln N_0-\lambda t<br />
\end{aligned}

    so the equation of the straight line is y=\ln N_0 -\lambda t. Acknowledged that the gradient is the coefficient which multiplies t and that the intercept is y(0), can you find these two constants ?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jisaac View Post
    The graph of radioactive count rate N against elapsed time t is an exponential; the equation of this graph is

    where N0 and λ are positive constants.

    A graph of ln N against t will be a straight line of gradient (something) and intercept of (something) on the vertical axis.

    what is the gradient and intercept?

    thanks!
    N = N_0 e^{- \lambda t}

    \Rightarrow \ln N = \ln (N_0 e^{- \lambda t})

    \Rightarrow \ln N = \ln N_0 + \ln (e^{- \lambda t})

    \Rightarrow \ln N = - \lambda t + \ln N_0

    now remember the slope-intercept form of the equation of a line. i leave the rest to you
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