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- Jun 23rd 2008, 12:08 PMjisaacGradient/intercept!
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- Jun 23rd 2008, 12:39 PMflyingsquirrel
Hello

$\displaystyle \begin{aligned}

\ln N&=\ln\left(N_0 \mathrm{e}^{-\lambda t}\right)\\

&=\ln N_0 + \ln \left( \mathrm{e}^{-\lambda t}\right)\\

&=\ln N_0-\lambda t

\end{aligned}$

so the equation of the straight line is $\displaystyle y=\ln N_0 -\lambda t$. Acknowledged that the gradient is the coefficient which multiplies $\displaystyle t$ and that the intercept is $\displaystyle y(0)$, can you find these two constants ? - Jun 23rd 2008, 12:40 PMJhevon
$\displaystyle N = N_0 e^{- \lambda t}$

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

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

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

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