## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by 4 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

## Comments

Sort by:

TopNewest\[\]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, 3 months ago

Log in to reply