A population is modeled by the differential equation $\frac { d P } { d t } = 0.4 P \left( 1 - \frac { P } { 250 } \right)$ where $P ( t )$ is the population at time $t$ .(a) What are the equilibrium solutions?
(b) For what values of $P$ is the population increasing?
(c) For what values of $P$ is the population decreasing?
(d) Use the information from above to sketch the direction field for the given differential equation.

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The Answer of A population is modeled by the differential equation $\frac { d P } { d t } = 0.4 P \left( 1 - \frac { P } { 250 } \right)$ where $P ( t )$ is the population at time $t$ .(a) What are the equilibrium solutions?
(b) For what values of $P$ is the population increasing?
(c) For what values of $P$ is the population decreasing?
(d) Use the information from above to sketch the direction field for the given differential equation.

A Population Is Modeled by the Differential Equation dPdt=0.4P(1−P250)\frac { d P } { d t } = 0.4 P \left( 1 - \frac { P } { 250 } \right)dtdP​=0.4P(1−250P​)

A Population Is Modeled by the Differential Equation $\frac { d P } { d t } = 0.4 P \left( 1 - \frac { P } { 250 } \right)$