Question

The rate of change of population $P(t)$ with respect to time $(t)$, where $\alpha$, $\beta$ are the constant birth and death rates, respectively, is

• A. $\dfrac{dP}{dt} = (\alpha + \beta)P$
• B. $\dfrac{dP}{dt} = (\alpha - \beta)P$
• C. $\dfrac{dP}{dt} = \dfrac{\alpha + \beta}{P}$
• D. $\dfrac{dP}{dt} = \dfrac{\alpha - \beta}{P}$

Hint:

In population models, net growth = birth rate $-$ death rate. Multiply this with current population for total rate of change.

Answer 1

The Correct Option is B

The rate of population change is the difference between the birth rate and death rate per unit population.
Birth adds individuals to the population, while death subtracts them.
So, $\text{Net Growth Rate} = \alpha - \beta$
The change in population is proportional to current population $P(t)$.
Hence, $\frac{dP}{dt} = (\alpha - \beta)P$