Assume That a Population Grows at a Rate Summarized by the Equation

Essay

Assume that a population grows at a rate summarized by the equation $\frac { d P } { d t } = \frac { b k P e ^ { - k t } } { 1 - b e ^ { - k t } }$ , where b and k are positive constants (b > 1), and P is the population at time t. Show that $P = \frac { P _ { o } } { 1 - b } \left( 1 - b e ^ { - k t } \right)$ is the general solution for the differential equation (where $P _ { o }$ is the initial population). [Note: This is known as the monomolecular growth curve.]