Wikipedia:Sandbox/Archive

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love father christmas xxx | testCyber Lopez Rt 10:33, 30 November 2006 (UTC)

$V=-{\frac {1}{\phi }}{\frac {dV}{dt}}$

${\frac {dV}{V}}=-\phi \ dt$

$\int _{V_{0}}^{V}\left({\frac {dV}{V}}\right)\ =\int _{0}^{t}(-\phi \ dt)$

$[\ln V]_{V_{0}}^{V}=-[\phi t]_{0}^{t}$

$\ln V-\ln V_{0}=-\phi t\,$

$\ln {\frac {V}{V_{0}}}=-\phi t$

${\frac {V}{V_{0}}}=e^{-\phi t}$

$V=V_{0}e^{-\phi t}\,$