The Autonomous Differential Equation Represents a Model for Population Growth $\frac { \mathrm { dP } } { \mathrm { dt } } = 1 - 8 \mathrm { P }$

Essay

The autonomous differential equation represents a model for population growth. Use phase line analysis to sketch solution curves for P(t), selecting different starting values P(0). Which equilibria are stable, and which are unstable?
- $\frac { \mathrm { dP } } { \mathrm { dt } } = 1 - 8 \mathrm { P }$