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.Find the size of the population P when the rate of change of the population is a minimum.(Remember P(0)= 1.)If there is no minimum rate of change, enter "DNE".

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.Find the size of the population P when the rate of change of the population is a minimum.(Remember P(0)= 1.)If there is no minimum rate of change, enter "DNE".

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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.Find the size of the population P when the rate of change of the population is a minimum.(Remember P(0)= 1.)If there is no minimum rate of change, enter "DNE".

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 $\frac{d P}{d t}=-0.05$