The rate of change of a population for a species is given by $\frac{d P}{d t}=-0.05$ P where P measures the population in thousands at time t months.The species starts with 1000 members (P = 1)at time t = 0.Assume that the differential equation holds indefinitely.If P = 0 is an equilibrium value of the population, is it stable or unstable? (If it is not an equilibrium value, enter "neither")

Question

The rate of change of a population for a species is given by $\frac{d P}{d t}=-0.05$ P   where P measures the population in thousands at time t months.The species starts with 1000 members (P = 1)at time t = 0.Assume that the differential equation holds indefinitely.If P = 0 is an equilibrium value of the population, is it stable or unstable? (If it is not an equilibrium value, enter "neither")

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The Answer of The rate of change of a population for a species is given by $\frac{d P}{d t}=-0.05$ P   where P measures the population in thousands at time t months.The species starts with 1000 members (P = 1)at time t = 0.Assume that the differential equation holds indefinitely.If P = 0 is an equilibrium value of the population, is it stable or unstable? (If it is not an equilibrium value, enter "neither")

The Rate of Change of a Population for a Species dPdt=−0.05\frac{d P}{d t}=-0.05dtdP​=−0.05

The Rate of Change of a Population for a Species $\frac{d P}{d t}=-0.05$