Question

If the initial size of a population was $N_o=10$ and the population is growing at the rate of 0.6%, when will the population stabilize? The carrying capacity of the population is 300.

• A. After 20 years
• B. A population having a positive growth rate will increase indefinitely
• C. When the population size is 300
• D. We can obtain the answer by solving for N in $\frac{dN}{dt}=0.6\times N\left(\frac{1-N}{300}\right)$ if $\frac{dN}{dt}$ had been given

Answer 1

The correct option is C

When the population size is 300

The carrying capacity of a population is the maximum sustainable population density, therefore a population stops growing once it reaches its carrying capacity. The carrying capacity here is 300, therefore the population stops growing and stabilizes when it reaches 300. When the population stabilizes $\frac{dN}{dt}$ is equal to zero, therfore if we solve the equation $\frac{dN}{dt}=0.6\times N\left(\frac{1-N}{300}\right)$, we get N = 300.