There is a differential equation that is a mathematical model of the situation in which the time rate of change in the population of a certain organism is proportional to the product of the current population and the difference between the current population and the limiting factor of 100,000. Is this the equation $\frac { \mathrm { dP } } { \mathrm { dt } } = \mathrm { kP } ( 100,000 - \mathrm { P } ) ?$

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This equation is a form of the logistic growth model, which describes how a population grows rapidly at first and then slows as it approaches a maximum limit, in this case, 100,000. The term $kP(100,000 - P)$ captures the essence of this behavior by incorporating both the growth rate (proportional to the current population $P$) and the limiting effect as $P$ approaches 100,000.

There Is a Differential Equation That Is a Mathematical Model dPdt=kP(100,000−P)?\frac { \mathrm { dP } } { \mathrm { dt } } = \mathrm { kP } ( 100,000 - \mathrm { P } ) ?dtdP​=kP(100,000−P)?

There Is a Differential Equation That Is a Mathematical Model $\frac { \mathrm { dP } } { \mathrm { dt } } = \mathrm { kP } ( 100,000 - \mathrm { P } ) ?$