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# logistic regression model

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Note by Insan Budiman Mahdar
4 years, 4 months 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 $$\,B=-r$$.

- 4 years, 1 month ago