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logistic regression model

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Note by Insan Budiman Mahdar
4 years, 1 month ago

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\[\]Try this one:\[\] \[ \begin{align} N_t&=\frac{K}{1+\left(\frac{K-N_0}{N_0}\right)e^{-rt}}\\ \left(\frac{K-N_0}{N_0}\right)e^{-rt}&=\frac{K}{N_t}-1\\ \left(\frac{K-N_0}{N_0}\right)e^{-rt}&=\left(\frac{K-N_t}{N_t}\right). \end{align} \] \[\]Let \(\,C=\left(\frac{K-N_0}{N_0}\right)\) and \(\,D=\left(\frac{K-N_t}{N_t}\right)\), then we have\[\] \[ \begin{align} Ce^{-rt}&=D\\ e^{-rt}&=\frac{D}{C}\\ \ln e^{-rt}&=\ln\left(\frac{D}{C}\right)\\ -rt&=\ln D-\ln C\\ \ln D&=\ln C-rt. \end{align} \] \[\]Final step, let \(\,Y=\ln D\), \(\,A=\ln C\), and \(\,B=-r\).

Tunk-Fey Ariawan - 3 years, 10 months ago

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