Question

How can the population be modeled from the equation and initial condition below?

$$\frac{dP}{dt}=2P\left(1-\frac{P}{68}\right),\quad P(0)=17$$

Accepted Answer

$$\begin{aligned}&	ext{Separate }\frac{dP}{P(1-\frac{P}{68})}=2\,dt\ &	ext{integrate and use }P(0)=17.\end{aligned}$$

Answer

$$	ext{Integrate }P	ext{ without first separating the variables.}$$

Answer

$$	ext{Discard the carrying capacity and use unrestricted exponential growth.}$$

Answer

$$	ext{Treat the derivative as a constant and fit a line.}$$

Practice: Integration - Logistic Growth Method