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

question 21

Short Answer

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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Definitions:

Herbivorous

An organism that feeds exclusively on plant materials, including leaves, stems, fruits, and roots.

Cnidarians

A phylum of aquatic invertebrates that includes jellyfish, corals, and sea anemones, known for their distinctive stinging cells called cnidocytes.

Gastropods

A large class of mollusks that include snails and slugs, characterized by a single shell (though some are shell-less) and a muscular foot for locomotion.

Ingest Food

The act of consuming food by mouth, initiating the process of digestion.