Question

Which of the differential equation represent the time rate of change a population P(t) with constant birth and death rate is proportional to the size of the population

Answer 1

Answer on Question #69666 – Math – Differential Equations

Question

Which of the differential equation represent the time rate of change a population $P(t)$ with constant birth and death rate is proportional to the size of the population.

Solution

For the closed system with constant birth and death rate is proportional to the size of the population, the time rate of change a population is given by

$$\frac{dP(t)}{dt} = (k_1 - k_2)P(t).$$

Here $k_1$ is the growth rate coefficient and $k_2$ is the death rate coefficient.

Answer: $\frac{dP(t)}{dt} = (k_1 - k_2)P(t)$.

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