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

Show Hint

In population models, net growth = birth rate $-$ death rate. Multiply this with current population for total rate of change.
  • $\dfrac{dP}{dt} = (\alpha + \beta)P$
  • $\dfrac{dP}{dt} = (\alpha - \beta)P$
  • $\dfrac{dP}{dt} = \dfrac{\alpha + \beta}{P}$
  • $\dfrac{dP}{dt} = \dfrac{\alpha - \beta}{P}$
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

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, $\frac{dP}{dt} = (\alpha - \beta)P$
Was this answer helpful?
0
0